Related papers: Representations of Lie Superalgebras in Prime Char…
Lie superautomorphisms of prime associative superalgebras are considered. A definitive result is obtained for central simple superalgebras: their Lie superautomorphisms are of standard forms, except when the dimension of the superalgebra in…
Given a Lie algebra $\mathfrak{g}$ of an algebraic group over a ring $S,$ we show that the first Kac-Weisfeiler conjecture holds for reductions of $\mathfrak{g} \mod p$ for large enough primes $p,$ reproving a recent result of Martin,…
The main goal of this paper is to develop the structure theory of Hom-Lie superalgebras in characteristic 2. We discuss their representations, semidirect product, $\alpha^k$-derivations and provide a classification in low dimension. We…
We overview the classifications of simple finite-dimensional modular Lie algebras. In characteristic 2, their list is wider than that in other characteristics; e.g., it contains desuperizations of modular analogs of complex simple vectorial…
In \cite{BKN} the authors initiated a study of the representation theory of classical Lie superalgebras via a cohomological approach. Detecting subalgebras were constructed and a theory of support varieties was developed. The dimension of a…
Some introductory concepts and basic definitions of the Lie superalgebras and their quantum deformations are exposed. Especially the induced representation methods in both cases are described. Based on the Kac representation theory we have…
Over a field of characteristic p>2, firstly, the structure of Kac modules of Lie superalgebra $\tilde{P}(2)$ and the weight space decompositions are given. Secondly, the weight-derivations of $\tilde{P}(2)$ to its Kac modules are computed.…
Atypicality is a fundamental combinatorial invariant for simple supermodules of a basic Lie superalgebra. Boe, Nakano, and the author gave a conjectural geometric interpretation of atypicality via support varieties. Inspired by low…
This paper is devoted to the study of Poisson superalgebras over fields of characteristic $2$. We investigate their representations, semidirect products, cohomology, formal deformations, and universal enveloping algebras. We also introduce…
This paper investigates cohomology and support varieties for Lie superalgebras and restricted Lie superalgebras over a field of characteristic 2. The existence of an underlying ordinary Lie algebra allows us to obtain results that are still…
Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is…
We give explicit formulas proving restrictedness of the following Lie (super)algebras: known exceptional simple vectorial Lie (super)algebras in characteristic 3, deformed Lie (super)algebras with indecomposable Cartan matrix, and (under…
This paper mainly studies the ResLieDer pair in characteristic 2, that is, a restricted Lie algebra with a restricted derivation. We define the restricted representation of a ResLieDer pair and the corresponding cohomology complex. We show…
A class of representations of a Lie superalgebra (over a commutative superring) in its symmetric algebra is studied. As an application we get a direct and natural proof of a strong form of the Poincare'-Birkhoff-Witt theorem, extending this…
We show that the Heisenberg Lie algebras over a field $\mathbb{F}$ of characteristic $p>0$ admit a family of restricted Lie algebras, and we classify all such non-isomorphic restricted Lie algebra structures. We use the ordinary 1- and…
Let k be an algebraically closed field of characteristic p> 0. For a basic classical Lie superalgebra, we show its restricted cohomology algebra is a finitely generated algebra. Thus the cohomological support theory can be established. As a…
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…
In this dissertation, we investigate the cohomology theory of restricted Lie algebras. The representation theory of restricted Lie algebras is reviewed including a description of the restricted universal enveloping algebra. In the case of…
It is generally believed (and for the most part is probably true) that Lie theory, in contrast to the characteristic zero case, is insufficient to tackle the representation theory of algebraic groups over prime characteristic fields.…
We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined…