Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras V defined by the identity y1(y2y3)(y4y5) ≡ 0. We give a complete description of the space of multilinear identities in the language of Young diagrams through the representation theory of the symmetric group. As an outcome we show that the variety V has almost polynomial growth, i.e., the sequence of codimensions of V cannot be bounded by any polynomial function but any proper subvariety of V has polynomial growth
MISHCHENKO, S, VALENTI A (2005). A Leibniz variety with almost polynomial growth. JOURNAL OF PURE AND APPLIED ALGEBRA, 202, 82-101.
A Leibniz variety with almost polynomial growth
VALENTI, Angela
2005-01-01
Abstract
Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras V defined by the identity y1(y2y3)(y4y5) ≡ 0. We give a complete description of the space of multilinear identities in the language of Young diagrams through the representation theory of the symmetric group. As an outcome we show that the variety V has almost polynomial growth, i.e., the sequence of codimensions of V cannot be bounded by any polynomial function but any proper subvariety of V has polynomial growth
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