An absolute parallelism for -nondegenerate CR manifolds of hypersurface type was recently constructed independently by Isaev-Zaitsev, Medori-Spiro, and Pocchiola in the minimal possible dimension (), and for in certain cases by the first author. We develop a bigraded analog of Tanaka's prolo…
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48 results for “nilpotent symbols”
Paper introduces a new symbol map for differential symmetry breaking operators.
problem Generalizing the symbol map to non-abelian settings.
method Introduces and studies the truncated symbol map .
result Classified and constructed differential intertwining operators and homomorphisms.
New CR hypersurfaces in complex space with specific properties.
problem Constructing CR hypersurfaces with arbitrary nilpotent symbols.
method Introduced a class of CR hypersurfaces with methods applicable to all cases with .
result Solved equivalence problem for structures with a single Jordan block symbol.
Study recovers C*-algebra from fields of Toeplitz algebras on specific groups.
problem Recovering C*-algebra from fields of Toeplitz algebras on specific groups.
method Using continuous fields of Toeplitz algebras and a crossed product.
result Algebra of principal symbols can be recovered from fields of Toeplitz algebras.
Researchers extend pseudodifferential calculus on filtered manifolds using fixed point algebras.
problem Defining operators with varying orders on filtered manifolds.
method Using generalized fixed point algebras and nilpotent Lie groups, they construct a new calculus.
result They establish a new calculus that reflects the behavior of differential operators on filtered manifolds.
Eisenhart's theorem extended to sub-Riemannian metrics on specific Lie algebras.
problem Extending Eisenhart's theorem to sub-Riemannian metrics on step 2 distributions.
method Introducing ad-surjective step 2 nilpotent Lie algebras and extending Eisenhart's theorem.
result The theorem holds for sub-Riemannian metrics on ad-surjective step 2 distributions.
Classifies homogeneous CR hypersurfaces in low dimensions with maximal symmetry.
problem Classifying CR hypersurfaces with maximal symmetry in low dimensions.
method Introduced modified CR symbols to organize local invariants, classified hypersurfaces through modified symbols, and used Lie group structures.
result Found nine model structures among locally homogeneous 2-nondegenerate hypersurfaces in .
Isomorphic algebra connects Toeplitz to Heisenberg group.
problem Connecting Toeplitz algebra to Heisenberg group.
method Isomorphism between Toeplitz algebra and Heisenberg group ideal.
result Found isomorphism between algebra and Heisenberg group ideal.
For q a root of unity of order 2r, we give explicit formulas of a family of 3-variable Laurent polynomials J_{i,j,k} with coefficients in Z[q] that encode the 6j-symbols associated with nilpotent representations of U_qsl_2. For a given abelian group G, we use them to produce a state sum invariant tau^r(M,L,h_1,h_2) of …
The paper studies how geometric transformations affect semi-classical operators on specific Lie groups.
problem Analyzing the effects of diffeomorphisms on semi-classical pseudodifferential operators.
method Examined the pull-back of semi-classical pseudodifferential operators by diffeomorphisms preserving the filtration.
result The pull-back of a semi-classical pseudodifferential operator by a Pansu differentiable diffeomorphism has a semi-classical symbol that is expressed in terms of the Pansu differential.
Isomorphism found between filtered calculus and crossed products.
problem Tackles isomorphism in filtered calculus and crossed products.
method Uses natural R-action and structure result for C*-algebra of graded nilpotent Lie groups.
result Found isomorphism between kernel of tangent groupoid and crossed product.
Unified approach to geometric structure equivalence problem.
problem Equivalence problem of geometric structures.
method Unified framework, step prolongation, structure function .
result Unified scheme for equivalence problem of geometric structures.
Nilpotent quandlesmath.GT
Nilpotent quandles have simple characterizations and are closely related to nilpotency.
problem Characterizing and understanding nilpotent quandles.
method Characterization of generating sets, Hopf property, construction of free nilpotent quandles, simple presentations of associated groups.
result Nilpotent quandles have the Hopf property and are equivalent to reduced peripheral systems.
Nilpotent Lie algebras obtained from ordered sets and quivers are algebraic Ricci solitons.
problem Constructing nilpotent Lie algebras as algebraic Ricci solitons
method Using transitively and antisymmetrically ordered sets (TAOSs) and incidence algebras
result Nilpotent Lie algebras with arbitrarily high degrees of nilpotency are algebraic Ricci solitons
New method constructs nilpotent Lie algebras from quivers.
problem Constructing nilpotent Lie algebras from quivers.
method Using paths within quivers to construct nilpotent Lie algebras.
result Constructs a broad family of Ricci soliton nilmanifolds.
Study knot invariants using automorphism groups of free nilpotent groups.
problem Developing knot invariants using automorphism groups.
method Nilpotently -localization of knot groups and automorphism groups of free nilpotent groups.
result Maps from outer automorphism groups yield knot invariants.
Nilpotent Sasakian manifolds are Heisenberg nilmanifolds.
problem Characterizing Sasakian manifolds with nilpotent fundamental groups.
method Proved diffeomorphism to Heisenberg nilmanifolds.
result Compact aspherical Sasakian manifolds with nilpotent fundamental groups are Heisenberg nilmanifolds.
We exhibit pseudo Riemannian manifolds which are Szabó nilpotent of arbitrary order, or which are Osserman nilpotent of arbitrary order, or which are Ivanov-Petrova nilpotent of order 3.
Classifies complex structures on specific nilpotent Lie algebras.
problem Classifying complex structures on nilpotent Lie algebras with minimal center.
method Classification through algebraic and geometric methods.
result Space of complex structures on specific Lie algebras up to isomorphism.
We compute the characteristic varieties and the Alexander polynomial of a finitely generated nilpotent group. We show that the first characteristic variety may be used to detect nilpotence. We use the Alexander polynomial to deduce that the only torsion-free, finitely generated nilpotent groups with positive deficiency…
VaSST uses soft symbolic trees for probabilistic symbolic regression.
problem Efficiently recover symbolic expressions from noisy data.
method Variational inference with soft symbolic trees.
result Superior performance in structural recovery and predictive accuracy.
This paper classifies Ricci soliton subgroups in a specific type of nilpotent group.
problem Classifying Ricci soliton subgroups in a specific type of nilpotent group.
method Using the properties of nilpotent Iwasawa groups and Lie subgroups.
result Classification of codimension one Lie subgroups of nilpotent Iwasawa groups that are Ricci solitons.
Study limits of adjoint orbits for Lie groups, describing nilpotent orbits.
problem Understanding limits of adjoint orbits for Lie groups.
method Systematic and topological study of limits of continuous families of adjoint orbits for non-compact simple Lie groups.
result Explicit description of nilpotent orbits in terms of Richardson orbits for hyperbolic semisimple elements.
Completes classification of G2-structures on specific nilpotent Lie groups.
problem Classifying seven-dimensional nilpotent Lie groups with purely coclosed G2-structures.
method Analyzing nilpotent Lie groups of various steps and dimensions.
result Classification of indecomposable 5- and 6-step nilpotent Lie groups.
New findings on complex structures in nilpotent Lie algebras and pseudo-Kähler geometry.
problem Classifying complex structures on nilpotent Lie algebras.
method Analysis of Lie algebras in dimensions eight and higher, identifying structures with pseudo-Kähler metrics.
result Identification of pseudo-Kähler nilmanifolds with invariant complex structures, providing counterexamples and topological restrictions.
The paper studies gradings on nilpotent Lie algebras linked to smooth algebraic varieties.
problem Understanding gradings on nilpotent Lie algebras associated with algebraic varieties.
method Analyzing lattice structures in nilpotent Lie groups and their fundamental groups.
result Conditions for a lattice to be the fundamental group of a smooth complex algebraic variety.
This paper completes the classification of certain nilpotent Lie groups with specific geometric structures.
problem Classifying nilpotent Lie groups with purely coclosed G2-structures.
method Analyzing seven-dimensional nilpotent Lie groups of various steps.
result Classification of indecomposable 5- and 6-step nilpotent Lie groups with these structures.
Criterion for nilpotent Lie groups to have nilsolitons.
problem Existence of nilsolitons in nilpotent Lie groups.
method Algebraic criterion for nilpotent Lie algebras, proving necessary and sufficient condition for nilsolitons.
result Criterion provides a necessary and sufficient condition for nilpotent Lie groups to admit nilsolitons.
We study complex product structures on nilpotent Lie algebras, establishing some of their main properties, and then we restrict ourselves to 6 dimensions, obtaining the classification of 6-dimensional nilpotent Lie algebras admitting such structures. We prove that any complex structure which forms part of a complex pro…
Study proves equality of LS-category and cohomological dimension for specific group homomorphisms.
problem Proving equality of LS-category and cohomological dimension for specific group homomorphisms.
method Analyzing epimorphisms and homomorphisms between specific types of almost nilpotent and virtually nilpotent groups.
result Equality of LS-category and cohomological dimension for specified group homomorphisms.
Study nilpotent Higgs bundles and Calabi-Yau moduli metrics.
problem Understand nilpotent Higgs bundles and their metrics.
method Algebraic inequality for nilpotent matrices, geometric applications.
result Sharp upper bound of holomorphic sectional curvatures on Calabi-Yau moduli.
This paper classifies strongly nilpotent special multi-flags and their Goursat counterparts.
problem Local classification of strongly nilpotent special multi-flags and Goursat distributions.
method Study of special multi-flags in homogeneous case, focusing on their weights.
result Strongly nilpotent germs of multiflags from different singularity classes are pairwise inequivalent.
Study on pseudo-Hermitian quadratic nilpotent Lie algebras with methods and classifications.
problem Characterizing and classifying pseudo-Hermitian quadratic nilpotent Lie algebras.
method Construction methods and double extension by planes.
result Complete classification of nilpotent quadratic Lie algebras and pseudo-Hermitian metrics up to dimension 8.
This article provides a complete description of the differential Gerstenhaber algebras of all nilpotent complex structures on any real six-dimensional nilpotent algebra. As an application, we classify all pseudo-Kählerian complex structures on six-dimensional nilpotent algebras such that the differential Gerstenhaber a…
Extends Floquet-Bloch theory to nilpotent groups for geometric applications.
problem Asymptotic problems on nilpotent covers of negatively curved manifolds.
method Generalized Floquet-Bloch theory using Malcev completions.
result Branching formula relating finite and infinite-dimensional representations.
Researchers determine Dehn functions of specific nilpotent groups.
problem Understanding the Dehn functions of central products of nilpotent groups.
method Analyzing families of filiform and Lie groups to determine Dehn functions.
result Confirms conjecture and provides evidence for lower Dehn functions in central products.
Gromov proposed an averaged version of the Dehn function and claimed that in many cases it should be subasymptotic to the Dehn function. Using results on random walks in nilpotent groups, we confirm this claim for most nilpotent groups. In particular, if a nilpotent group satisfies the isoperimetric inequality $δ(l)<Cl…
We study the question of the existence of left-invariant Sasaki contact structures on the seven-dimensional nilpotent Lie groups. It is shown that the only Lie group allowing Sasaki structure with a positive definite metric tensor is the Heisenberg group. We find a complete list of the 22 classes of seven-dimensional n…
We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP. However, in problems with large number of variables, we find that by constraini…
Classifies nilpotent Lie groups with specific -structures.
problem Identifying 7D nilpotent Lie groups with purely coclosed -structures.
method Examined all 7D nilpotent Lie algebras, classified them, and verified the existence or non-existence of -structures.
result Provided a complete classification of 7D nilpotent Lie groups with purely coclosed -structures.
Study torsion-free nilpotent fundamental groups of smooth varieties up to rank 7.
problem Characterize fundamental groups of smooth quasi-projective varieties.
method Analyzes fundamental groups of smooth quasi-projective varieties using topological and Lie group theory.
result Determine fundamental groups for smooth quasi-projective varieties up to rank 7.
A near-identity nilpotent pseudogroup of order m >= 1 is a family f_1, ..., f_n: (-1,1) -> R of C^2 functions for which: |f_i - id|_{C^1} < epsilon for some small positive real number epsilon < 1/10^{m+1} and commutators of the functions f_i of order at least m equal the identity. We present a classification of near-id…
Paper closes neural-symbolic learning loop with grammar model and back-search algorithm.
problem Slow convergence in neural-symbolic learning due to error propagation issues.
method Introduces grammar model as symbolic prior and back-search algorithm for efficient error propagation.
result Significantly outperforms RL methods in performance, converging speed, and data efficiency.
A nonpolycyclic nilpotent-by-cyclic group Gamma can be expressed as the HNN extension of a finitely-generated nilpotent group N. The first main result is that quasi-isometric nilpotent-by-cyclic groups are HNN extensions of quasi-isometric nilpotent groups. The nonsurjective injection defining such an extension induces…
Reinforcement learning and symbolic planning have both been used to build intelligent autonomous agents. Reinforcement learning relies on learning from interactions with real world, which often requires an unfeasibly large amount of experience. Symbolic planning relies on manually crafted symbolic knowledge, which may …
The study characterizes G₂-structures on 2-step nilpotent Lie groups.
problem Characterizing G₂-structures on 2-step nilpotent Lie groups.
method Analyzing left-invariant purely coclosed G₂-structures on 7-dimensional 2-step nilpotent Lie groups.
result Criteria for Riemannian metrics induced by these structures and determination of isomorphism classes.
In this paper we attempt to give a systematic account on privileged coordinates and the nilpotent approximation of Carnot manifolds. By a Carnot manifold it is meant a manifold with a distinguished filtration of subbundles of the tangent bundle which is compatible with the Lie bracket of vector fields. This paper lies …
New definition of Rumin complex for nilpotent Lie groups.
problem No new problem introduced.
method Alternative definition of Rumin complex on nilpotent Lie groups.
result Direct application of cohomology results to all nilpotent Lie groups.