Formula derived for Lie algebra E8's bracket.
problem Calculating the bracket of the exceptional Lie algebra E8.
method Based on triality and oct-octonions, following Barton-Sudbery description.
result Explicit formula for E8's bracket.
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48 results for “Lie algebra E8”
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.)
We study isometric Lie group actions on the compact exceptional groups E6, E7, E8, F4 and G2 endowed with a biinvariant metric. We classify polar actions on these groups. We determine all isometric actions of cohomogeneity less than three on E6, E7, F4 and all isometric actions of cohomogeneity less than 20 on E8. More…
Classifies real trivectors in 9D using Galois cohomology.
problem Classifying real trivectors in R^9.
method Galois cohomology, theta-representations, centralizers computation.
result Classification of real trivectors into nilpotent, semisimple, and mixed types.
The compact exceptional Lie groups F4, E6, E7 and E8 have spinor groups as a subgroup as follows: E8 \supset Ss(16) \supset Spin(15) \supset Spin(14) \supset Spin(13), E7 \supset Spin(12) \supset Spin(11), E6 \supset Spin(10), F4 \supset Spin(9) \supset Spin(8) \supset Spin(7) \supset \cdot \cdot \cdot \supset Spin(1) …
New anomaly cancellation formulas for E8*E8*E8 gauge group.
problem Anomaly cancellation for E8*E8*E8 gauge group.
method Constructed modular forms over SL2(Z) to get new anomaly cancellation formulas.
result New anomaly cancellation formulas for characteristic forms.
The notion of (Z/2Z) x (Z/2Z)-symmetric spaces is a generalization of classical symmetric spaces, where the group Z/2Z is replaced by (Z/2Z) x (Z/2Z). In this article, a classification is given of the (Z/2Z) x (Z/2Z)-symmetric spaces G/K where G is an exceptional compact Lie group or Spin(8), complementing recent resul…
New formulas derived for anomaly cancellation using modular forms and E8 bundles.
problem Anomaly cancellation in odd dimensions.
method Systematic twisting and generalization of SL(2,Z) modular forms to define new forms associated with E8 and E8*E8 bundles.
result Derivation of a new series of anomaly cancellation formulas.
New anomaly formulas from E8 bundles.
problem Anomaly cancellation in characteristic forms.
method Constructing modular forms using E8 bundles.
result New anomaly cancellation formulas.
Complete construction for Lie groups of types F4, E6, E7, E8.
problem Provide coordinates for surface representations into Lie groups of all types.
method Cluster ensemble framework, triangulated 3-manifolds, Fomin-Zelevinsky work.
result Complete construction for Lie groups of types F4, E6, E7, E8.
New anomaly formulas derived from bundles.
problem Anomaly cancellation in characteristic forms.
method Constructing modular forms over specific groups using bundles.
result Derived new anomaly cancellation formulas.
In this note we revisit the subject of anomaly cancelation in string theory and M-theory on manifolds with String structure and give three observations. First, that on String manifolds there is no E8 x E8 global anomaly in heterotic string theory. Second, that the description of the anomaly in the phase of the M-theory…
New hyperKähler orbifolds of Kummer type discovered.
problem Identifying new compact hyperKähler orbifolds.
method Construction of orbifolds and analysis of singularities.
result Only orbifolds with known holomorphic symplectic resolutions lead to known hyperKähler 8-manifolds.
Characterizes Lie groups with specific structures and finds a correspondence between carrollian and galilean Lie algebras.
problem Understanding Lie groups with specific structures.
method Using structure theory of metric Lie algebras and defining new Lie algebras with skew-symmetric derivations.
result A canonical correspondence between carrollian and galilean Lie algebras mediated by bargmannian Lie algebras.
Develops a bialgebra theory for post-Lie algebras using geometric interpretations and bilinear forms.
problem Characterizing and understanding post-Lie algebras and their associated structures.
method Utilizes Manin triples and generalized Hessian Lie groups to define and characterize post-Lie algebras with nondegenerate symmetric invariant bilinear forms.
result Establishes a bialgebra theory for post-Lie algebras via the Manin triple approach, including new algebraic structures like pp-post-Lie algebras.
In this paper, we present a study on the prolongations of representations of Lie algebras. We show that a tangent bundle of a given Lie algebra attains a Lie algebra structure. Then, we prove that this tangent bundle is algebraically isomorphic to the Lie algebra of a tangent bundle of a Lie group. Using these, we defi…
A Lie-admissible algebra gives by anticommutativity a Lie algebra. In this work we study remarkable classes of Lie-admissible algebras such as Vinberg, PreLie algebras. We compute the corresponding binary quadratic operads and study their Koszul duality. Considering Lie algebras as Lie-admissible algebras we can define…
The paper generalizes para-Kähler Lie algebras to k-para-Kähler Lie algebras and explores their structures.
problem Characterizing and understanding k-para-Kähler Lie algebras.
method Generalization of para-Kähler Lie algebras to k-para-Kähler Lie algebras, introduction of new structures, determination of Lie algebras.
result Determination of all k-symplectic Lie algebras of dimension (k+1) and six-dimensional 2-para-Kähler Lie algebras.
We introduce post-Lie algebra structures on pairs of Lie algebras $(\Lg,\Ln)$ defined on a fixed vector space . Special cases are LR-structures and pre-Lie algebra structures on Lie algebras. We show that post-Lie algebra structures naturally arise in the study of NIL-affine actions on nilpotent Lie groups. We obtai…
Study on pre-Lie structures for semisimple Lie algebras over C.
problem Admissibility of pre-Lie structures in semisimple Lie algebras.
method Examined properties of anti-flexible algebras (AFAs), computed Lie-admissibility criteria, and provided examples.
result Explicit counterexample of an AFA admissible by sl(2, C).
We construct the Lie algebra of an n-Lie algebra and we also define the notion of cohomology of an n-Lie algebra.
The aim of this note is to introduce the notion of a -Lie algebra and to prove some elementary properties of -Lie algebras, the category of -Lie algebras, the category of modules on a -Lie algebra and extensions of -Lie algebras. …
Lie's Third Theorem, asserting that each finite-dimensional Lie algebra is the Lie algebra of a Lie group, fails in infinite dimensions. The modern account on this phenomenon is the integration problem for central extensions of infinite-dimensional Lie algebras, which in turn is phrased in terms of an integration proce…
Lie algebroids and curved Lie algebras are equivalent categories.
problem Understanding the relationship between Lie algebroids and curved Lie algebras.
method Developed a method to study the -category of curved Lie algebras using homotopy theory of algebras over a complete operad.
result Equivalence of -categories between Lie algebroids and certain kinds of curved Lie algebras.
In this paper, we introduce the notion of a (regular) Hom-Lie group. We associate a Hom-Lie algebra to a Hom-Lie group and show that every regular Hom-Lie algebra is integrable. Then, we define a Hom-exponential (Hexp) map from the Hom-Lie algebra of a Hom-Lie group to the Hom-Lie group and discuss the universality of …
A pseudo -type Lie algebra naturally gives rise to a conformal pseudo-subriemannian fundamental graded Lie algebras. In this paper we investigate the prolongations of the associated fundamental graded Lie algebra and the associated conformal pseudo-subriemannian fundamental graded Lie algebra. In particular, we show…
If a Lie algebra structure g on a vector space is the sum of a family of mutually compatible Lie algebra structures g_i's, we say that g is simply assembled from the g_i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the g_i's, one obtains a Lie algebra assembled in two step…
New Lie algebras from knot homology.
problem Defining Lie algebras from knot homology.
method Using group homology, analogous to Goldman Lie algebra.
result Relations among new Lie algebras discussed.
A new category of Lie algebras, called generalized Lie algebras, is presented such that classical Lie algebras and Lie-Rinehart algebras are objects of this new category. A new philosophy over generalized Lie algebroids theory is presented using the notion of generalized Lie algebra and examples of objects of the categ…
Symmetric spaces' connections form Lie admissible triple algebras.
problem Understanding the algebraic structure of symmetric spaces' connections.
method Analyzing the connection as a binary operator on tangent bundle sections, identifying Lie admissibility constraints.
result Connection algebra of symmetric spaces is a Lie admissible triple algebra.
Proofs centerless unimodular contact Lie algebras.
problem Characterizing centerless unimodular contact Lie algebras.
method Elementary proof and introduction of DS-contact Lie algebras.
result The only centerless unimodular examples are and .
The strong symmetric genus of a finite group G is the smallest genus of a closed orientable topological surface on which G acts faithfully as a group of orientation preserving automorphisms. In this paper we complete the calculation of the strong symmetric genus for each finite Coxeter group excluding the group E8.
Lie groups of automorphisms of cotangent bundles of Lie groups are completely characterized and interesting results are obtained. We give prominence to the fact that the Lie groups of automorphisms of cotangent bundles of Lie groups are super symmetric Lie groups. In the cases of orthogonal Lie lgebras, semi-simple Lie…
Characterizes G2-structures on Lie algebras with non-trivial center.
problem Classifying Lie algebras with G2-structures.
method Analyzing Lie algebras with non-trivial center, using contactization and symplectic properties.
result Six unimodular Lie algebras with non-trivial center admit closed G2-structures.
Factorizable Lie bialgebras, quadratic Rota-Baxter Lie algebras and Rota-Baxter Lie bialgebrasmath-ph
The paper connects Lie bialgebras, Rota-Baxter Lie algebras, and their properties.
problem Exploring connections between Lie bialgebras and Rota-Baxter Lie algebras.
method Introducing quadratic Rota-Baxter Lie algebras, matched pairs, bialgebras, and Manin triples.
result Established a correspondence between factorizable Lie bialgebras and quadratic Rota-Baxter Lie algebras.
Study on generalized derivations in polynomial vector fields Lie algebras.
problem Understanding generalized derivations in specific Lie sub-algebras of polynomial vector fields.
method Analysis of Lie sub-algebras containing constant and Euler vector fields, under specified conditions.
result Characterization of generalized derivations in the studied Lie sub-algebras.
Study coKähler structures on Lie algebras using Fino-Vezzoni correspondence.
problem Characterize coKähler structures on Lie algebras.
method Use Fino-Vezzoni correspondence to relate coKähler Lie algebras to Kähler Lie algebras.
result Complete the flat case for odd-dimensional Lie algebras, proving coKähler structures exist.
Born Lie algebrasmath.DG
Born Lie algebras classified up to 6D, with integrable metrics studied.
problem Classifying and understanding Born Lie algebras.
method Bicross product construction from pseudo-Riemannian Lie algebras.
result Classification of Lie algebras up to 6D with integrable Born structures.
Study cohomology of hemistrict Lie 2-algebras, proving isomorphic results.
problem Understanding cohomology of hemistrict Lie 2-algebras.
method Functorial construction and isomorphism proof of cohomology.
result Cohomology of hemistrict Lie 2-algebras is isomorphic to Chevalley-Eilenberg cohomology.
Study locally conformally balanced metrics on specific Lie algebras.
problem Characterize and classify locally conformally balanced metrics on almost abelian Lie algebras.
method Characterizations and classifications based on specific properties of Lie algebras.
result Classification of six-dimensional almost abelian Lie algebras with locally conformally balanced metrics.
Abstract: Connections between Lie algebras and symplectic nilmanifolds explored.
problem Understanding the relationship between Lie algebras and symplectic nilmanifolds.
method Central extensions of Lie algebras, dynamical systems, and symplectic nilmanifolds constructed.
result Covering Lie groups for symplectic nilmanifolds can have any rank as solvable Lie groups.
The paper studies the center of the Goldman Lie algebra and its properties.
problem Identifying the center of the Goldman Lie algebra and its properties.
method Analyzing the Goldman Lie algebra as a Z_2-graded Lie algebra and using properties of the even part.
result The center of the even part of the Goldman Lie algebra is generated by specific classes of loops.
The paper investigates gradings of complex simple Lie algebras, focusing on -gradings and their algebraic structures.
problem Investigating the algebraic structure of -gradings of complex simple Lie algebras.
method Completely determining the possible reductive algebras and proving the uniqueness of a specific free nilpotent Lie algebra.
result The only free nilpotent Lie algebra of step 3 that appears as the negative part of a -grading is the usual -grading of the exceptional Lie algebra .
This research introduces Lie brackets on spaces of biderivations in Lie algebras.
problem Understanding higher-order infinitesimal symmetries in Lie algebras.
method Study of right biderivations and Lie brackets on their spaces.
result New Lie algebra framework for biderivations with applications in deformation theory.
2-compatible Lie algebras are quadratic deformations of Lie algebras with specific constraints.
problem Classifying contact Lie algebras using quadratic deformations.
method Defining 2-compatible Lie algebras as quadratic deformations of Lie algebras and studying the constraints on these deformations.
result Any (2p+1)-dimensional contact Lie algebra is isomorphic to a quadratic deformation of the Heisenberg algebra.
Study on pseudo-Riemannian algebraic Ricci solitons in 4D Lie groups.
problem Investigating conditions for pseudo-Riemannian algebraic Ricci solitons on 4D Lie algebras.
method Analyzing the algebraic Ricci soliton equation for each 4D Lie algebra.
result Complete description of pseudo-Riemannian algebraic Ricci solitons in dimension four.
We study post-Lie algebra structures on pairs of Lie algebras (g,n), and prove existence results for the case that one of the Lie algebras is semisimple. For semisimple g and solvable n we show that there exist no post-Lie algebra structures on (g,n). For semisimple n and certain solvable g we construct canonical post-…
A Lie version of Turaev's -Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a \textit{-quasi-Frobenius Lie algebra} for a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius…