6533b851fe1ef96bd12a8fcf

RESEARCH PRODUCT

A Leibniz variety with almost polynomial growth

S. MishchenkoA. Valenti

subject

symbols.namesakePure mathematicsAlgebra and Number TheoryInvariant polynomialSymmetric polynomialAlternating polynomialLeibniz formula for determinantsHomogeneous polynomialsymbolsElementary symmetric polynomialPolarization of an algebraic formMathematicsSquare-free polynomial

description

Abstract Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras V ˜ 1 defined by the identity y 1 ( y 2 y 3 ) ( y 4 y 5 ) ≡ 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 ˜ 1 has almost polynomial growth, i.e., the sequence of codimensions of V ˜ 1 cannot be bounded by any polynomial function but any proper subvariety of V ˜ 1 as polynomial growth.

yearjournalcountryeditionlanguage
2005-11-01Journal of Pure and Applied Algebra
https://doi.org/10.1016/j.jpaa.2005.01.013