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.
Abstract: Geometrically reformulates estimation theory for finite-dimensional C*-algebras.
Lie's third theorem proven for Lie ∞-algebras.
We prove that there is no faithful finite-dimensional representation by skew-hermitian matrices of a ``basic algebra of observables'' B on a noncompact symplectic manifold M. Consequently there exists no finite-dimensional quantization of any Lie subalgebra of the Poisson algebra C^\infty(M) containing B.
Classifies vector field algebras in complex space.
New groups algebraically fibre with high-dimensional hyperbolic groups.
This paper provides a stratification of semi-algebraic sets in the plane with finitely many geodesic segments.
Compute central extension of mapping class group from stated skein algebra
The Kuperberg invariant is shown to be gauge invariant for certain framed 3-manifolds.
The purpose of this paper is to show how central extensions of (possibly infinite-dimensional) Lie algebras integrate to central extensions of étale Lie 2-groups. In finite dimensions, central extensions of Lie algebras integrate to central extensions of Lie groups, a fact which is due to the vanishing of π_2 for each …
The paper deals with amoebas of -dimensional algebraic varieties in the algebraic complex torus of dimension . First, we show that the area of complex algebraic curve amoebas is finite. Moreover, we give an estimate of this area in the rational curve case in terms of the degree of the rational parametrizat…
Automorphisms of finite order and real forms of "smooth" affine Kac-Moody algebras are studied, i.e. of 2-dimensional extensions of the algebra of smooth loops in a simple Lie algebra. It is shown that they can be parametrized by certain invariants and that in particular the classification of involutions essentially fo…
New theory disassembles Lie algebras into dyons and triadons.
The paper gives the complete characterization of all graded nilpotent Lie algebras with infinite-dimensional Tanaka prolongation as extensions of graded nilpotent Lie algebras of lower dimension by means of a commutative ideal. We introduce a notion of weak characteristics of a vector distribution and prove that if a b…
Maximal cubic quotient of braid algebra studied for n ≤ 5.
Characterizes algebraic integrability and minimality of Lie equations for non-commutative pseudogroups.
Defines complex manifolds on commutative Banach algebras and studies continuous families of compact complex manifolds.
Local description of solvable Lie algebras of vector fields.
It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by open-closed two-dimensional topological field theories. In this paper we extend o…
Enhances conformal geometry in higher dimensions with infinite-dimensional algebra.
The paper describes the K-theory of -algebras of locally finite graphs.
For finite dimensional real Lie algebras, we investigate the existence of an inner product having a basis comprised of geodesic elements. We give several existence and non-existence results in certain cases: unimodular solvable Lie algebras having an abelian nilradical, algebras having an abelian derived algebra, algeb…
Integrates Leibniz algebras into Lie racks.
Paper connects two invariants of 3D manifolds using Hopf algebras.
Following I. S. Krasilshchik and A. M. Vinogradov, we regard PDEs as infinite-dimensional manifolds with involutive distributions and consider their special morphisms called differential coverings, which include constructions like Lax pairs and Backlund transformations. We show that, similarly to usual coverings in top…
There is a remarkable and canonical problem in 3D geometry and topology: To understand existing models of 3D fluid motion or to create new ones that may be useful. We discuss from an algebraic viewpoint the PDE called Euler's equation for incompressible frictionless fluid motion. In part I we define a "finite dimension…
Researchers create explicit representations for skein algebras of small surfaces, revealing their Azumaya loci.
The semidirect product of a Lie algebra and a 2-term representation up to homotopy is a Lie 2-algebra. Such Lie 2-algebras include many examples arising from the Courant algebroid appearing in generalized complex geometry. In this paper, we integrate such a Lie 2-algebra to a strict Lie 2-group in the finite dimensiona…
Classifies symplectic Lie algebras and their associated manifolds.
Study algebraic relations of Vassiliev invariants for families of knots.
In math.DG/0312243 we developed a general classification scheme for metric Lie algebras, i.e. for finite-dimensional Lie algebras equipped with a non-degenerate invariant inner product. Here we determine all nilpotent Lie algebras l with dim l'=2 which are used in this scheme. Furthermore, we classify all nilpotent met…
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 global symmetry algebras of partially-massless (PM) higher-spin (HS) fields in (A)dS are studied. The algebras involving PM generators up to depth are defined as the maximal symmetries of free conformal scalar field with order wave equation in dimensions. We review the constructi…
Study Lie algebras of indefinite spaces with finite volume.
We explicitly compute the lower algebraic K-theory of the split three-dimensional crystallographic groups; i.e., the groups G that act properly and cocompactly on three-dimensional Euclidean space by isometries, such that the natural map from G to O(3) is a split injection onto its image. There are 73 split three-dimen…
We show how to construct the nonstandard hull of certain infinite-dimensional Lie algebras in order to generalize a theorem of Pestov on the enlargeability of Banach-Lie algebras. In the process, we consider a nonstandard smoothness condition on functions between locally convex spaces to ensure that the induced functio…
Proposes a new gauge theory for fuzzy geometries using finite-dimensional algebras.
Direct proof for Duflo isomorphism for arbitrary Lie algebras.
Study on Mackenzie obstruction for transitive Lie algebroids, proving triviality for certain Lie algebras.
Riemannian symmetric spaces are fundamental objects in finite dimensional differential geometry. An important problem is the construction of symmetric spaces for generalizations of simple Lie groups, especially their closest infinite dimensional analogues known as Kac-Moody groups. We solve this problem and construct a…
The paper proves a category of dg manifolds with finite positive amplitude.
We define an action of Artin's braid group on a finite dimensional algebra.
Every finite dimensional real representation of a compact real semisimple Lie algebra determines a metric 2-step nilpotent Lie algebra and a corresponding simply connected metric 2-step nilpotent Lie group N. We study the differential geometry of N using representation theory of the complexified complex semisimple Lie …
Generalizes pseudo-product structures with abnormal extremals.
We discuss locally simply transitive affine actions of Lie groups G on finite-dimensional vector spaces such that the commutator subgroup [G,G] is acting by translations. In other words, we consider left-symmetric algebras satisfying the identity [x,y].z=0. We derive some basic characterizations of such left-symmetric …
New conditions for weighted composition operators in group homomorphisms.
Study isometries of Clifford algebras over real numbers.
The paper studies spaces of non-compact real algebraic curves and their uniformisation.
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to those of the infinite dihedral group, we give the algebra the name iD-infinity.