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The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

Abanina, L., Mishchenko, S. (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras 3N determined by the identity x(y(zt)) ≡ 0. The algebras of this variety are left nilpotent of class not more than 3. We give a complete description of the vector space of multilinear identities in the language of representation theory of the symmetric group Sn and Young diagrams. We also show that the...

Weak polynomial identities and their applications

Vesselin Drensky (2021)

Communications in Mathematics

Let R be an associative algebra over a field K generated by a vector subspace V . The polynomial f ( x 1 , ... , x n ) of the free associative algebra K 〈 x 1 , x 2 , ... 〉 is a weak polynomial identity for the pair ( R , V ) if it vanishes in R when evaluated on V . We survey results on weak polynomial identities and on their applications to polynomial identities and central polynomials of associative and close to them nonassociative algebras and on the finite basis problem. We also present results on weak polynomial identities of degree three....

Weak Polynomial Identities for M1,1(E)

Di Vincenzo, Onofrio, La Scala, Roberto (2001)

Serdica Mathematical Journal

* Partially supported by Universita` di Bari: progetto “Strutture algebriche, geometriche e descrizione degli invarianti ad esse associate”.We compute the cocharacter sequence and generators of the ideal of the weak polynomial identities of the superalgebra M1,1 (E).

Z2-Graded Polynomial Identities for Superalgebras of Block-Triangular Matrices

Di Vincenzo, Onofrio (2004)

Serdica Mathematical Journal

000 Mathematics Subject Classification: Primary 16R50, Secondary 16W55.We present some results about the Z2-graded polynomial identities of block-triangular matrix superalgebras R[[A M],[0 B]]. In particular, we describe conditions for the T2-ideal of a such superalgebra to be factorable as the product T2(A)T2(B). Moreover, we give formulas for computing the sequence of the graded cocharacters of R in some interesting case.Partially supported by MURST COFIN 2003 and Università di Bari.

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