A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Simple construction of Rumin algebra for contact manifolds.
High-order Klein geometries constructed using Lie algebras.
One of the methods to obtain Frobenius manifold structures is via DGBV (differential Gerstenhaber-Batalin-Vilkovisky) algebra construction. An important problem is how to identify Frobenius manifold structures constructed from two different DGBV algebras. For DGBV algebras with suitable conditions, we show the functori…
New tools for studying Hsiang algebras discovered, linking them to known algebraic structures.
In this work, the Z-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. universal enveloping algebra of the quantum plane is explicitly constructed and an isomorphism between the quantum Lie algeb…
Develops method to construct Lie algebra weight system kernel using Vogel algebra.
Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be the simplicial Lie group integrating g, which is simply connected in each simplicial level. We use the 1-jet of the classifying space of G to construct, starting from g, a Lie k-algebra L. The so constructed Lie k-algebra L is actually a diff…
Constructs Lie-Rinehart algebra for Einstein's equations.
We present a construction of invariants for links using an isomorphism theorem for affine Yokonuma--Hecke algebras. The isomorphism relates affine Yokonuma--Hecke algebras with usual affine Hecke algebras. We use it to construct a large class of Markov traces on affine Yokonuma--Hecke algebras, and in turn, to produce …
Constructs Lie algebras from labeled directed graphs and identifies properties of these algebras.
A Chern-Weil construction for extensions of Lie-Rinehart algebras is introduced. This generalizes the classical Chern-Weil construction in differential geometry and yields characteristic classes for arbitrary extensions of Lie-Rinehart algebras. Some examples arising from spaces with singularities and from foliations a…
Study cohomology of hemistrict Lie 2-algebras, proving isomorphic results.
New method constructs nilpotent Lie algebras from quivers.
Paper constructs super integrable systems on color Lie algebra.
We define a torus algebra for Heegaard Floer homology.
Paper constructs observables using multisymplectic geometry and algebraic methods.
Witt algebra acts on categorified quantum groups in type A.
We construct the Lie algebra of an n-Lie algebra and we also define the notion of cohomology of an n-Lie algebra.
We construct a Hopf action, with an invariant trace, of a bicrossed product Hopf algebra $\cH=\big( \cU(\Fg_1) \acr \cR(G_2) \big)^{\cop}$ constructed from a matched pair of Lie groups and , on a convolution algebra $\cA=C_c^{\ify}(G_1)\rtimes G_2^δ$. We give an explicit way to construct Hopf cyclic cohomolo…
Variant of previous work on smooth algebraic functions with compact and non-compact preimages.
We define a differential graded algebra for Legendrian graphs and tangles in the standard contact Euclidean three space. This invariant is defined combinatorially by using ideas from Legendrian contact homology. The construction is distinguished from other versions of Legendrian contact algebra by the vertices of Legen…
Researchers prove Lie algebras of differential operators and Grothendieck constructions coincide.
New algebra for twice-punctured torus curves.
We investigate Lie algebras endowed with a complex symplectic structure and develop a method, called \emph{complex symplectic oxidation}, to construct certain complex symplectic Lie algebras of dimension from those of dimension . We specialize this construction to the nilpotent case and apply complex symplec…
We consider Drinfeld-Sokolov bihamiltonian structure associated to a distinguished nilpotent elements of semisimple type and the space of common equilibrium points defined by its leading term. On this space, we construct a local bihamiltonian structure which form an exact Poisson pencil, defines an algebraic classical …
Using crossed homomorphisms, we show that the category of weak representations (resp. admissible representations) of Lie-Rinehart algebras (resp. Leibniz pairs) is a left module category over the monoidal category of representations of Lie algebras. In particular, the corresponding bifunctor of monoidal categories is e…
The paper constructs new algebraic structures from Lie algebras and ternary Nambu-Lie algebras, leading to Yang-Baxter operators.
Study SKT and Kähler structures on specific Lie algebras.
New algebraic structures called cyclic Lie-Rinehart algebras are defined.
Vogel's construction links knot invariants to Lie algebras, revealing new insights.
Construct spectral triples on C*-algebras with group actions.
In the 90s, based on presentations of 3-manifolds by Heegaard diagrams, Kuperberg associated a scalar invariant of 3-manifolds to each finite dimensional involutory Hopf algebra over a field. We generalize this construction to the case of involutory Hopf algebras in arbitrary symmetric monoidal categories admitting cer…
Constructs local superconformal algebras on supermanifolds.
We construct an algebra of smooth functions over the tangent groupoid associated to any Lie groupoid. This algebra is a field of algebras over the closed interval [0, 1] which fiber at zero is the algebra of Schwartz functions over the Lie algebroid, whereas any fiber out of zero is the convolution algebra of the initi…
Geometrically constructs Virasoro-Bott group from circle diffeomorphisms.
New discrete cobordism category for nested manifolds and relations to algebraic structures.
Statistical Lie algebras with constant curvature are linked to locally conformally Kähler structures.
The paper extends algebraic constructions to -graded manifolds and Lie algebroids.
Jacobi/Poisson algebras are algebraic counterparts of Jacobi/Poisson manifolds. We introduce representations of a Jacobi algebra and Frobenius Jacobi algebras as symmetric objects in the category. A characterization theorem for Frobenius Jacobi algebras is given in terms of integrals on Jacobi algebras. For a vecto…
Nilpotent Lie algebras obtained from ordered sets and quivers are algebraic Ricci solitons.
Abstract: Connections between Lie algebras and symplectic nilmanifolds explored.
In this article, we define and study the affine and cyclotomic Yokonuma-Hecke algebras. These algebras generalise at the same time the Ariki-Koike and affine Hecke algebras and the Yokonuma-Hecke algebras. We study the representation theory of these algebras and construct several bases for them. We then show how we can…
We show that the skew-symmetrized product on every Leibniz algebra E can be realized on a reductive complement to a subalgebra in a Lie algebra. As a consequence, we construct a nonassociative multiplication on E which, when E is a Lie algebra, is derived from the integrated adjoint representation. We apply this constr…
Based on representation theory of Clifford algebra, Ferus, Karcher and Münzner constructed a series of isoparametric foliations. In this paper, we will survey recent studies on isoparametric hypersurfaces of OT-FKM type and investigate related geometric constructions with mean curvature flow.
Develops differential K-theory for noncommutative algebras.
Using the technique of higher derived brackets developed by Voronov, we construct a homotopy Loday algebra in the sense of Ammar and Poncin associated to any symplectic -manifold. The algebra we obtain has a particularly nice structure, in that it accommodates the Dorfman bracket of a Courant algebroid as the binary…
Characterizes a specific type of Courant algebroid with a Calabi-Yau structure.
Defines and extends flat pseudo-Riemannian F-Lie algebras.