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.
Study coKähler structures on Lie algebras using Fino-Vezzoni correspondence.
Constructs Lie algebras from labeled directed graphs and identifies properties of these algebras.
Graph Lie algebras have infinite prolongation if they have a vertex of degree one.
New method finds invariants of Lie algebras, especially for semi-direct sums.
New method constructs nilpotent Lie algebras from quivers.
We study local ()-webs of codimension 1 on a manifold of dimension We give a complete description of their possible Lie algebras of infinitesimal diffeomorphisms. More precisely we show that these Lie algebras are direct products of sub-algebras which are isomorphic to to the non-commutative 2…
Characterizes non-degenerate cyclic metric Lie algebras.
Uniform Lie algebras are combinatorially defined two-step nilpotent Lie algebras which can be used to define Einstein solvmanifolds. These Einstein spaces often have nontrivial isotropy groups. We derive basic properties of uniform Lie algebras and we classify uniform Lie algebras with five or fewer generators. We defi…
Motivated by Kohno's result on the holonomy Lie algebra of a hyperplane arrangement, we define the holonomy Lie algebra of a finite geometric lattice in a combinatorial way. For a solvable pair of lattices, we show that the holonomy Lie algebra is an almost-direct product of the holonomy Lie algebra of the sublattice a…
Deforms orbits in Lie algebras to Lagrangian submanifolds.
Decomposable arrangements have simpler topological and combinatorial properties.
If a Lie algebra structures $\gG$ on a vector space is the sum of a family of mutually compatible Lie algebra structures $\gG_i$, we say that $\gG$ is \emph{simply assembled} from $\gG_s$'s. By repeating this procedure several times one gets a family of Lie algebras \emph{assembled} from $\gG_s$'s. The central result o…
The paper studies nice bases for Lie algebras and their properties.
Classifies geodesic vectors in low-dimensional Lie algebras.
We analyze symplectic forms on six dimensional real solvable and non-nilpotent Lie algebras. More precisely, we obtain all those algebras endowed with a symplectic form that decompose as the direct sum of two ideals or are indecomposable solvable algebras with a four dimensional nilradical.
Higher-dimensional Milnor frames are characterized and contrasted with 3D Heisenberg and 4D nilpotent Lie algebras.
We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixe…
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…
Proof of injection from double shuffle to Kashiwara-Vergne Lie algebra.
Researchers prove Lie algebras of differential operators and Grothendieck constructions coincide.
Dani and Mainkar introduced a method for constructing a 2-step nilpotent Lie algebra from a simple directed graph in 2005. There is a natural inner product on arising from the construction. We study geometric properties of the associated simply connected 2-step nilpotent Lie group …
New Lie algebras from quivers lead to rigid Ricci solitons.
We explore the graded and filtered formality properties of finitely generated groups by studying the various Lie algebras over a field of characteristic 0 attached to such groups, including the Malcev Lie algebra, the associated graded Lie algebra, the holonomy Lie algebra, and the Chen Lie algebra. We explain how thes…
In this paper, first we introduce the notion of a phase space of a 3-Lie algebra and show that a 3-Lie algebra has a phase space if and only if it is sub-adjacent to a 3-pre-Lie algebra. Then we introduce the notion of a product structure on a 3-Lie algebra using the Nijenhuis condition as the integrability condition. …
Nilpotent Lie algebras obtained from ordered sets and quivers are algebraic Ricci solitons.
Study various series of groups and their Lie algebras in split extensions.
Courant algebroids are structures which include as examples the doubles of Lie bialgebras and the direct sum of tangent and cotangent bundles with the bracket introduced by T. Courant for the study of Dirac structures. Within the category of Courant algebroids one can construct the doubles of Lie bialgebroids, the infi…
In this paper we discuss the question of integrating differential graded Lie algebras (DGLA) to differential graded Lie groups (DGLG). We first recall the classical problem of integration in the context, and present the construction for (non-graded) differential Lie algebras. Then, we define the category of differentia…
Eisenhart's theorem extended to sub-Riemannian metrics on specific Lie algebras.
We give a global picture of the Ricci flow on the space of three-dimensional, unimodular, nonabelian metric Lie algebras considered up to isometry and scaling. The Ricci flow is viewed as a two-dimensional dynamical system for the evolution of structure constants of the metric Lie algebra with respect to an evolving or…
Classifies Lie algebras and related spacetimes for a specific type of symmetry.
Quantum neural networks need both data-dependent and trainable unitaries for effective geometric deformation.
Generalizations in many directions of the contraction procedure for Lie algebras introduced by E.J.Saletan are proposed. Products of arbitrary nature, not necessarily Lie brackets, are considered on sections of finite-dimensional vector bundles. Saletan contractions of such infinite-dimensional algebras are obtained vi…
The paper integrates Rota-Baxter Lie algebras into Lie group structures and geometries.
A 2-step nilpotent Lie algebra n is called nonsingular if ad(X): n --> [n,n] is onto for any X not in [n,n]. We explore nonsingular algebras in several directions, including the classification problem (isomorphism invariants), the existence of canonical inner products (nilsolitons) and their automorphism groups (maxima…
Researchers establish a connection between knot homology and Lie algebra actions.
Three new types of graded Lie groups are constructed and analyzed.
Let G be a Lie group, its cotangent bundle with its natural Lie group structure obtained by performing a left trivialization of T^*G and endowing the resulting trivial bundle with the semi-direct product, using the coadjoint action of G on the dual space of its Lie algebra. We investigate the group of automorphi…
The paper explores associative structures in pseudo-Riemannian Lie algebras and their geometric implications.
During the last decades algebraization of space turned out to be a promising tool at the interface between Mathematics and Theoretical Physics. Starting with works by Gel'fand-Kolmogoroff and Gel'fand-Naimark, this branch developed as from the fortieth in two directions: algebraic characterization of usual geometric sp…
We prove that a vector bundle is characterized by the Lie algebra generated by all differential operators on which are eigenvectors of the Lie derivative in the direction of the Euler vector field. Our result is of Pursell-Shanks type but it is remarkable in the sense that it is the whole fibration tha…
The existence of a flat torsion-free connection, or left symmetric algebra structure on a Lie algebra g gives rise to a canonically defined complex structure on g+g and a symplectic structure on g+g^*. We verify that the associated differential Gerstenhaber algebras controlling the deformation theories of the complex a…
New method preserves MHD equations on sphere without costly matrix exponentials.
We consider semi-direct products $\C^{n}\ltimes_φN$ of Lie groups with lattices such that are nilpotent Lie groups with left-invariant complex structures. We compute the Dolbeault cohomology of direct sums of holomorphic line bundles over by using the Dolbeaut cohomology of the Lie algebras of the direct …
We explain a direct topological proof for the multiplicativity of Duflo isomorphism for arbitrary finite dimensional Lie algebras, and derive the explicit formula for the Duflo map. The proof follows a series of implications, starting with "the calculation 1+1=2 on a 4D abacus", using the study of homomorphic expansion…
The preprint is prepared as description of results that were obtained during joint scientific project No: 71NC /2015/VNCCCT on the VIASM (Vietnam Institute for Advanced Study in Mathematics) from 08.12.2015 to 06.02.2016. The problem was formulated how to calculate so called the Mackenzie obstruction for existing of tr…
In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie subgroups, and integrability of Lie algebra extensions to Lie group extensions. We furthe…
For a real, non-singular, 2-step nilpotent Lie algebra , the group \Aut(\mathfrak{n})/\Aut_0(\mathfrak{n})\Aut_0(\mathfrak{n})$ is the group of automorphisms which act trivially on the center, is the direct product of a compact group with the 1-dimensional group of dilations. Maximality of some …