A class of Lie and Jordan algebras realized by means of the canonical commutation relations
A review of Lie superalgebra cohomology for pseudoforms
This note is based on a short talk presented at the “42nd Winter School Geometry and Physics” held in Srni, Czech Republic, January 15th–22nd 2022. We review the notion of Lie superalgebra cohomology and extend it to different form complexes, typical of the superalgebraic setting. In particular, we introduce pseudoforms as infinite-dimensional modules related to sub-superalgebras. We then show how to extend the Koszul-Hochschild-Serre spectral sequence for pseudoforms as a computational method to...
An introduction to some novel applications of Lie algebra cohomology in mathematics and physics.
En esta nota se presenta en primer lugar una introducción autocontenida a la cohomología de álgebras de Lie, y en segundo lugar algunas de sus aplicaciones recientes en matemáticas y física.
Application of the Gel'fand matrix method to the missing label problem in classical kinematical Lie algebras.
Arithmetic features of rational conformal field theory
Conformal blocks in the tensor product of vector representations and localization formulas
Using equivariant localization formulas we give a formula for conformal blocks at level one on the sphere as suitable polynomials.
Contractions of Lie algebras and algebraic groups
Degenerations, contractions and deformations of various algebraic structures play an important role in mathematics and physics. There are many different definitions and special cases of these notions. We try to give a general definition which unifies these notions and shows the connections among them. Here we focus on contractions of Lie algebras and algebraic groups.
Enveloping algebras of Slodowy slices and the Joseph ideal
Let be a simple algebraic group over an algebraically closed field of characteristic 0, and . Let be an -triple in with being a long root vector in . Let be the -invariant bilinear form on with and let be such that for all . Let be the Slodowy slice at through the adjoint orbit of and let be the enveloping algebra of ; see [31]. In this article we give an explicit presentation of by generators and relations. As a consequence we deduce that contains an ideal...
First-order differential invariants of the splitting subgroups of the Poincaré group .
Fixed Points and D-branes
Free field construction of D-branes in rational models of CFT and Gepner models.
From Poisson algebras to Gerstenhaber algebras
Constructing an even Poisson algebra from a Gerstenhaber algebra by means of an odd derivation of square 0 is shown to be possible in the category of Loday algebras (algebras with a non-skew-symmetric bracket, generalizing the Lie algebras, heretofore called Leibniz algebras in the literature). Such “derived brackets” give rise to Lie brackets on certain quotient spaces, and also on certain Abelian subalgebras. The construction of these derived brackets explains the origin of the Lie bracket on...
Fusion algebras for superconformal field theories through coinvariants. II: super-Virasoro-symmetry.
Homotopy Rinehart cohomology of homotopy Lie-Rinehart pairs.
Lie group analysis of mixed convection flow with mass transfer over a stretching surface with suction or injection.
Maximal solvable extensions of filiform algebras
It is already known that any filiform Lie algebra which possesses a codimension 2 solvable extension is naturally graded. Here we present an alternative derivation of this result.
Monstrous moonshine and monstrous Lie superalgebras.
On brane solutions related to non-singular Kac-Moody algebras.
On representations of Lie algebras of a generalized Tavis-Cummings model.
On solutions of the KZ and qKZ equations at level zero