Related papers: The classification of almost affine (hyperbolic) L…

Let U(L) be the enveloping algebra of a finite dimensional Lie algebra L over a field k of characteristic zero, Z(U(L)) its center and Sz(U(L)) its semicenter. A sufficient condition is given in order for Sz(U(L)) to be a polynomial algebra…

The finite dimensional simple modular Lie algebras with Cartan matrix cannot be deformed if the characteristic p of the ground field is equal to 0 or greater than 3. If p=3, the orthogonal Lie algebra o(5)is one of the two simple modular…

Let $B$ be a $\mathbb{Z}$-graded Lie superalgebra equipped with an invariant $\mathbb{Z}_2$-symmetric homogeneous bilinear form and containing a grading element. Its local part (in the terminology of Kac) $B_{-1} \oplus B_{0} \oplus B_{1}$…

For a large class of finite-dimensional Lie superalgebras (including the classical simple ones) a Lie supergroup associated to the algebra is defined by fixing the Hopf superalgebra of functions on the supergroup. Then it is shown that on…

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…

This paper deals with affine connections on real manifolds. We give a new characterization of flat affine connections on real manifolds by means of certain affine representations of the Lie group of automorphisms preserving the connection.…

We show that Automorphic Lie Algebras which contain a Cartan subalgebra with a constant spectrum, called hereditary, are completely described by 2-cocycles on a classical root system taking only two different values. This observation…

This paper considers a family of finite dimensional simple Lie superalgebras of Cartan type over a field of characteristic $p>3$, the so-called special odd contact superalgebras. First, the spanning sets are determined for the Lie…

Any graded restricted simple Lie algebra of Cartan type contains a subalgebra isomorphic to the Witt algebra over a field of prime characteristic. As some analogue of study on branching rules for restricted non-classical Lie algebras, it is…

For a Lie superalgebra with Cartan matrix over a field of positive characteristic, some information about its root system in terms of the system of simple roots corresponding to the Chevalley generators is described, under certain given…

Elie Cartan's general equivalence problem is recast in the language of Lie algebroids. The resulting formalism, being coordinate and model-free, allows for a full geometric interpretation of Cartan's method of equivalence via reduction and…

For modular Lie superalgebras, new notions are introduced: Divided power homology and divided power cohomology. For illustration, we give presentations (in terms of analogs of Chevalley generators) of finite dimensional Lie (super)algebras…

We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley--Sohoni Geometric Complexity Theory program. A matrix Lie…

We construct four new series of generalized simple Lie algebras of Cartan type, using the mixtures of grading operators and down-grading operators. Our results in this paper are further generalizations of those in Osborn's work ``New simple…

We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description of their extension groups. Furthermore, we describe the block…

This paper describes finite dimensionall irreducible representations of both twisted and untwisted Cartan map Lie superalgebras.

In the first part of my talk I will explain a solution to the extension of Lie's problem on classification of "local continuous transformation groups of a finite-dimensional manifold" to the case of supermanifolds. (More precisely, the…

Recently one of the authors obtained a classification of simple infinite-dimensional Lie superalgebras of vector fields which extends the well-known classification of E. Cartan in the Lie algebra case. The list consists of many series…

Suppose a group $\Gamma$ acts on a scheme $X$ and a Lie superalgebra $\mathfrak{g}$. The corresponding equivariant map superalgebra is the Lie superalgebra of equivariant regular maps from $X$ to $\mathfrak{g}$. We classify the irreducible…

The essential feature of a root-graded Lie algebra L is the existence of a split semisimple subalgebra g with respect to which L is an integrable module with weights in a possibly non-reduced root system S of the same rank as the root…