Related papers: Gradings on the Kac superalgebra

We give a complete derived equivalence classification of all nonstandard representation-infinite domestic selfinjective algebras over an algebraically closed field. As a consequence, also a complete stable equivalence classification of…

We present a classification of the hyperbolic Kac-Moody (HKM) superalgebras. The HKM superalgebras of rank larger or equal than 3 are finite in number (213) and limited in rank (6). The Dynkin-Kac diagrams and the corresponding simple root…

We give classifications of group gradings, up to equivalence and up to isomorphism, on the tensor product of a Cayley algebra $\mathcal{C}$ and a Hurwitz algebra over a field of characteristic different from 2. We also prove that the…

We classify gradings on the Hecke category that refine the standard integer grading. We also classify object-preserving autoequivalences of the Hecke category. We obtain a natural bigrading on the Hecke category which is related to the…

It is known that the category of Lie algebras over a ring admits algebraic exponents. The aim of this paper is to show that the same is true for the category of internal Lie algebras in an additive, cocomplete, symmetric, closed, monoidal…

We list classical spherical subalgebras in basic matrix Lie superalgebras which are quantizable to coideal subalgebras in the standard quantum supergroups, for any choice of Borel subalgebra. We classify the corresponding Satake-type…

In this paper we give a complete classification of cyclically graded semisimple Lie algebras that afford cuspidal character sheaves and determine the support of the cuspidal character sheaves. This constitutes a major step towards the…

Categories over a field $k$ can be graded by different groups in a connected way; we consider morphisms between these gradings in order to define the fundamental grading group. We prove that this group is isomorphic to the fundamental group…

Kac's ten-dimensional simple Jordan superalgebra over a field of characteristic 5 is obtained from a process of semisimplification, via tensor categories, from the exceptional simple Jordan algebra (or Albert algebra), together with a…

This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the varieties of Jordan, Lie and associative algebras.

In this paper we give the complete classification of $5$-dimensional complex solvable symmetric Leibniz algebras.

We classify simple linearly compact n-Lie superalgebras with n>2 over a field F of characteristic 0. The classification is based on a bijective correspondence between non-abelian n-Lie superalgebras and transitive Z-graded Lie superalgebras…

We describe a collection of differential graded rings that categorify weight spaces of the positive half of the quantized universal enveloping algebra of the Lie superalgebra gl(1|2).

We introduce a new class of graded rings extending the class of generalized Weyl algebras. These rings are orders in crossed products of the most general type, and we introduce their basic structure theory. We provide an extensive list of…

In a Hom-Malcev algebra an identity, equivalent to the Hom-Malcev identity, is found.

A catalogue of explicit realizations of representations of (super) Lie algebras and quantum algebras in Fock space is presented.

We classify all the hyperspherical equivariant slices of reductive groups. The classification is $S$-dual to the one of basic classical Lie superalgebras.

We introduce a notion of Krein C*-module over a C*-algebra and more generally over a Krein C*-algebra. Some properties of Krein C*-modules and their categories are investigated.

The so called quantized algebras of functions on affine Hecke algebras of type A and the corresponding q-Schur algebras are defined and their irreducible unitarizable representations are classified.

Let $n$ be a positive integer, and let $R$ be a (possibly infinite dimensional) finitely presented algebra over a computable field of characteristic zero. We describe an algorithm for deciding (in principle) whether $R$ has at most finitely…