Killing-Yano and conformal Killing-Yano superalgebras are rigid in constant curvature manifolds.
problem Understanding the rigidity of Killing-Yano and conformal Killing-Yano superalgebras in constant curvature manifolds.
method Defining Z-gradations and filtrations, showing trivial second cohomology groups, and proving non-deformability. result Killing-Yano and conformal Killing-Yano superalgebras are rigid and correspond to geometric invariants of constant curvature manifolds.
Researchers study Killing superalgebras in 2D manifolds.
problem Characterizing Killing superalgebras in 2D pseudo-Riemannian manifolds.
method Computing Spencer cohomology and filtered deformations of superalgebras.
result Killing superalgebras arise as solutions for geometric and skew-Killing spinors.
This paper classifies Killing superalgebras for Lorentzian 4-manifolds.
problem Understanding Killing superalgebras in Lorentzian 4-manifolds.
method Reinterpreting as filtered deformations of subalgebras, computing Spencer cohomology, identifying Killing spinors.
result Maximally supersymmetric backgrounds are classified based on their Killing superalgebras.
Study the algebraic structure of Killing superalgebras in 11D supergravity.
problem Classify highly supersymmetric backgrounds.
method Mapped classification problem to filtered deformations of graded subalgebras of Poincaré superalgebra.
result Reconstructing backgrounds from Killing superalgebras and relating to field equations.
Extends symmetry superalgebras to include all hidden symmetries of manifolds.
problem Tackles hidden symmetries of manifolds generated by Killing spinors.
method Defines generalized symmetry superalgebras, constructs Lie algebra structure, and defines symmetry operators.
result Constructs special Killing-Yano and conformal Killing-Yano forms from bilinears of Killing spinors.
Extends Killing superalgebras to higher dimensions and signatures.
problem Generalizing Killing superalgebras to higher dimensions and signatures.
method Definition of Killing superalgebras for connections on spinor bundles, sufficient conditions for existence, abstract study using Spencer cohomology.
result Existence of Killing superalgebras as filtered deformations of graded subalgebras of the Poincaré superalgebra.
Researchers develop new symmetry operators from conformal Killing-Yano forms.
problem Constructing symmetry operators for twistor spinors in conformally-flat backgrounds.
method Using conformal Killing-Yano forms and graded Lie algebra structure, the researchers extended conformal superalgebras to include twistor spinors.
result Extended conformal superalgebras that include twistor spinors and conformal Killing-Yano forms are constructed.
Extended superalgebras from twistor and Killing spinors in constant curvature and Einstein manifolds.
problem Constructing extended superalgebras from twistor and Killing spinors.
method Using twistor and Killing spinors, symmetry operators, and KY/CKY forms, extended superalgebras are constructed.
result Extended Killing and conformal superalgebras are constructed in constant curvature and Einstein manifolds.
Defines Killing spinors and bosonic backgrounds in 5D supergravity.
problem Characterizing backgrounds in 5D supergravity.
method Calculates Spencer cohomology, defines Killing spinors, and imposes constraints on spinor connection curvature.
result Recover field equations of 5D supergravity and find new field equations for sp(1)-valued one-form. Researchers calculate superalgebras for six-dimensional Lorentzian manifolds.
problem Understanding rigidly supersymmetric geometries in six dimensions.
method Calculating Spencer cohomology of (1,0) Poincaré superalgebras. result Maximally supersymmetric backgrounds identified, including Lorentzian Lie groups.
Defines Killing (super)algebras for spin manifolds, including gauge transformations.
problem Understanding deformations of spin structures on manifolds.
method Introduces a new algebraic structure, studies its deformations using Spencer cohomology.
result Identifies subclasses of deformations and reconstructs supersymmetric backgrounds.
Proves Minkowski flux backgrounds preserve supersymmetry and relate to special holonomy.
problem Relating Minkowski flux backgrounds to special holonomy manifolds.
method Introducing Kosmann-Dorfman bracket and Killing superalgebra.
result Generic Minkowski flux backgrounds preserving N supersymmetries correspond to integrable generalised G_N structures.
We determine the holonomy of generalized Killing spinor covariant derivatives of the form D=∇+Ω on pseudo-Riemannian reductive homogeneous spaces in a purely algebraic and algorithmic way, where Ω:TM→Λ∗(TM) is a left-invariant homomorphism. This is essentially an application of the theory of i…
We use the manifestly conformally invariant description of a Lorentzian conformal structure in terms of a parabolic Cartan geometry in order to introduce a superalgebra structure on the space of twistor spinors and normal conformal vector fields formulated in purely algebraic terms on parallel sections in tractor bundl…
We present a geometric construction of the exceptional Lie algebras F4 and E8 starting from the round 8- and 15-spheres, respectively, inspired by the construction of the Killing superalgebra of a supersymmetric supergravity background. (There is no supergravity in the paper.)
Study of AdS backgrounds preserving supersymmetry using generalised geometry.
problem Characterize AdS backgrounds preserving supersymmetry.
method Use generalised geometry to study supersymmetric AdS backgrounds of eleven-dimensional or type II supergravity.
result Show that a class of AdS backgrounds correspond to spaces with weak generalised holonomy.
We prove that supersymmetry backgrounds of (1,0) and (2,0) six-dimensional supergravity theories preserving more than one half of the supersymmetry are locally homogeneous. As a byproduct we also establish that the Killing spinors of such a background generate a Lie superalgebra.
The super or Z_2-graded Schouten-Nijenhuis bracket is introduced. Using it, new generalized super-Poisson structures are found which are given in terms of certain graded-skew-symmetric contravariant tensors Λof even order. The corresponding super `Jacobi identities' are expressed by stating that these tensors have zero…
We present a maximally supersymmetric IIB string background. The geometry is that of a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous five-form flux. We give the explicit supergravity solution, compute the isometries, the 32 Killing spinors, and the symmetry superalgebra, and then d…
Combines supergeometry and supersymmetry for new geometric structures.
problem Combining supergeometry and supersymmetry for new geometric structures.
method Constructs special supermanifolds and defines supersymmetric Killing structures.
result Defines a new algebra that extends supersymmetry to non-flat spaces.
New homogeneous M2 brane duals found for specific dimensions.
problem Finding new gravity duals for M2 branes with enhanced supersymmetry.
method Classifying homogeneous M-theory backgrounds with specific symmetry algebras.
result Several new backgrounds with n=5 found, some of which are supersymmetric. Spin geometry reviewed with applications in physics.
problem None explicitly stated, but related to spin geometry and its applications.
method Definitions of spin geometry, Clifford algebras, and spinors; discussion of differential operators, twistor and Killing spinors; holonomy classification; construction of symmetry operators and extended superalgebras.
result Construction of extended superalgebras and methods to find solutions of Seiberg-Witten equations.
Study connects derivations and holonomy symmetries in heterotic geometries.
problem Understanding the algebra of derivations and holonomy symmetries in heterotic geometries.
method Analyzing the superalgebra of derivations and exploring the relation to holonomy symmetries in sigma models.
result Proposed Lie bracket on the space of fundamental forms and derivation algebras for heterotic geometries.
The paper proves rigidity results for certain supergravity backgrounds in 11 dimensions.
problem Supersymmetry gap problem for supergravity backgrounds in 11 dimensions.
method Study of curvature restrictions and use of bijective correspondence between filtered deformations of Lie superalgebras and highly supersymmetric backgrounds.
result Rigidity results for specific supergravity backgrounds with low rank 4-form and high Killing spinor dimension.
The study examines conditions for completeness and simplicity in hom-Lie superalgebras.
problem Conditions for completeness and simplicity in hom-Lie superalgebras.
method Equivalent conditions and derivations analysis.
result Conditions for completeness and simplicity in hom-Lie superalgebras.
The paper defines Z-graded hom-Lie superalgebras and explores their properties.
problem Understanding the structure and properties of Z-graded hom-Lie superalgebras.
method Definition and exploration of Z-graded hom-Lie superalgebras, invariant bilinear forms, and simplicity conditions.
result Maximal and minimal Z-graded hom-Lie superalgebras for local hom-Lie superalgebras are identified, and conditions for simplicity are checked.
Classifies low-dimensional 3-Lie superalgebras.
problem Classifying low-dimensional 3-Lie superalgebras.
method Using induced Lie superalgebras and Clifford algebras with Z_2-graded structures.
result Explicit description of 3-Lie superalgebras by ternary commutators.
New invariant for 3-manifolds from topological Hopf superalgebra.
problem Constructing an invariant for 3-manifolds.
method Using a ribbon superalgebra from a topological Hopf superalgebra, we construct an invariant of 3-manifolds of Hennings type.
result Constructs a new invariant for 3-manifolds from a topological Hopf superalgebra.
Starting from the four normed division algebras - the real numbers, complex numbers, quaternions and octonions - a systematic procedure gives a 3-cocycle on the Poincare Lie superalgebra in dimensions 3, 4, 6 and 10. A related procedure gives a 4-cocycle on the Poincare Lie superalgebra in dimensions 4, 5, 7 and 11. In…
The paper introduces transposed Poisson superalgebras and their properties.
problem Developing algebraic structures for quantum physics.
method Defining transposed Poisson superalgebras using derivations and proving their identities.
result Six identities are crucial for understanding transposed Poisson superalgebras.
Recent work applying higher gauge theory to the superstring has indicated the presence of `higher symmetry'. Infinitesimally, this is realized by a `Lie 2-superalgebra' extending the Poincare superalgebra in precisely the dimensions where the classical supersymmetric string makes sense: 3, 4, 6 and 10. In the previous …
Study uses superalgebra homology to classify 4D Engel-like Lie algebras.
problem Classifying 4-dimensional Engel-like Lie algebras.
method Applied homology groups of Lie superalgebras.
result Distinguished and classified 4D Engel-like Lie algebras.
Study pseudo-Riemannian metrics on Jordan superalgebras.
problem No specific problem stated; focus on metrics.
method Coadjoint orbit-like construction for pseudo-Euclidean Jordan superalgebras.
result Investigated canonical pseudo-Riemannian metrics.
Study Euler and Betti numbers of homology groups for a specific type of superalgebra.
problem Calculating Euler and Betti numbers for homology groups of pre Lie superalgebras.
method Introduced double weighted chain spaces to analyze pre Lie superalgebras of multi-vector fields with polynomial coefficients. Calculated Euler and Betti numbers for these homology groups.
result Derived formulas for Euler and Betti numbers of homology groups of pre Lie superalgebras.
Two geometric realizations of F(4) Lie superalgebra found.
problem Geometric realization of F(4) Lie superalgebra. method Explicit geometric realizations as supersymmetries of super-PDE systems.
result Two orders of super-PDE systems found for F(4). From the four normed division algebras--the real numbers, complex numbers, quaternions and octonions, of dimension k=1, 2, 4 and 8, respectively--a systematic procedure gives a 3-cocycle on the Poincare superalgebra in dimensions k+2=3, 4, 6 and 10, and a 4-cocycle on the Poincare superalgebra in dimensions k+3=4, 5, 7…
Symplectic spinors and their properties are analyzed for Hodge theory.
problem Decomposing and characterizing symplectic spinors and their derivatives.
method Representation theory, cohomology, and duality of Lie superalgebras.
result Valid Hodge theory for elliptic complexes involving symplectic spinors.
We determine the structure of the ∗-Lie superalgebra generated by a set of carefully chosen natural operators of an orientable WSD manifold of rank three. This Lie superalgebra is formed by global sections of a natural Lie superalgebra bundle, and turns out to be a product of $\mathbf{sl}(4,\C)$ with the full special…
New cohomology groups generalize Euler number for Lie superalgebras.
problem Generalizing cohomology groups for Lie superalgebras.
method Abstracted Poisson cohomology groups to Poisson-like cohomology groups for general Lie superalgebras.
result De Rham cohomology groups match Poisson-like cohomology groups for differential forms.
New q-series found for osp(2|2n) Lie superalgebra.
problem Finding a q-series invariant for osp(2|2n).
method Invariant series for 3-manifolds associated with Lie superalgebras.
result A q-series found for osp(2|2n).
Paper computes Lie superalgebras of vector fields on flag supermanifolds.
problem Computing Lie superalgebras of vector fields on flag supermanifolds.
method Analyzes complex flag supermanifolds introduced by Yu.I.Manin.
result Holomorphic vector fields are fundamental with respect to glm∣n(C). These notes record three lectures given at the workshop "Higher symmetries in Physics", held at the Universidad Complutense de Madrid in November 2008. In them we explain how to construct a Lie (super)algebra associated to a spin manifold, perhaps with extra geometric data, and a notion of privileged spinors. The typic…
Paper shows how a Lie superalgebra can be realized using matrices.
problem Realizing the Lie superalgebra of contact projective vector fields.
method Using embedding techniques from projectively equivariant quantizations, the paper constructs a matrix realization.
result The Lie superalgebra spo(2l+2∣n) is realized as the intersection of pgl(2l+2∣n) and K(2l+1∣n). Derives 11D supergravity from filtered subdeformations of Poincaré superalgebra.
problem Deriving 11D supergravity from algebraic structures.
method Lie-algebraic derivation of 11D supergravity from filtered subdeformations of Poincaré superalgebra.
result Derives 11D supergravity from algebraic structures.
We describe explicitly Lie superalgebra isomorphisms between the Lie superalgebras of first-order superdifferential operators on supermanifolds, showing in particular that any such isomorphism induces a diffeomorphism of the supermanifolds. We also prove that the group of automorphisms of such a Lie superalgebra is a s…
The paper realizes Lie superalgebras G(3) and F(4) as symmetries of supergeometries.
problem Addressing whether exceptional Lie superalgebras G(3) and F(4) are maximal symmetries of supergeometries.
method Considering negatively graded Lie superalgebras for every choice of parabolic subgroup, computing Tanaka-Weisfeiler prolongations, and reducing the structure group when required.
result Realization of 19 inequivalent G(3)-supergeometries and 55 inequivalent F(4)-supergeometries.
Unified approach to decomposing commutative n-ary superalgebras with skew-symmetric forms.
problem Decomposing commutative n-ary superalgebras with skew-symmetric invariant forms.
method Unified approach using derived bracket formalism and inductive orthogonal sums and generalized double extensions.
result Any commutative n-ary superalgebra with a skew-symmetric invariant form can be obtained by inductive orthogonal sums and generalized double extensions.
The study explores Lie superalgebras constructed from Lie algebras using Schouten-like brackets.
problem Investigate how the core Lie algebra controls the Lie superalgebra.
method Construct Lie superalgebras from abstract Lie algebras using Schouten-like brackets and analyze Betti numbers of super homology groups.
result For low dimensional non-abelian Lie algebras, the Betti numbers of super homology groups provide insights into the control of the core Lie algebra.