Group gradings on superalgebras
In this paper we look into the structure of finite-dimensional graded superalgebras of various types such as associative, Lie and Jordan over an algebraically closed field of characteristic zero.
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arXiv subjects
T. Tvalavadze
Publications and source records attributed to T. Tvalavadze.
Group gradings on superinvolution simple superalgebras
In this paper we describe all group gradings by an arbitrary finite group $G$ on non-simple finite-dimensional superinvolution simple associative superalgebras over an algebraically closed field $F$ of characteristic 0 or coprime to the order of $G$.
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Simple decompositions of simple Lie superalgebras
In this paper we consider Lie superalgebras decomposable as the sum of two proper subalgebras. Any of these algebras has the form of the vector space sum $L=A+B$ where $A$ and $B$ are proper simple subalgebras which need not be ideals of $L$, and the sum need not be direct. The main result of this paper is the following: Let $S = {osp}(m,2n)$ be a Lie superalgebra such that $S=K+L$ where $K$, $L$ are two proper basic simple subalgebras. Then $m$ is even, $m=2k$ and $K \cong osp(2k-1,2n)$, $L \cong sl(k,n)$.
math.RA↗