Identities of relatively free algebras of Lie nilpotent associative algebras

2025/03/28 by Hristova, Elitza, de Mello, Thiago Castilho
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2503.22664

Abstract

In this paper, we consider the relatively free algebra of rank n, F_n(\mathfrakN_p), in the variety of Lie nilpotent associative algebras of index p, denoted by \mathfrakN_p, over a field of characteristic zero. We describe an explicit minimal basis for the polynomial identities of F_n(\mathfrakN_p) when p=3 and p=4, for all n, except for F₃(\mathfrakN₄). In the general case, we exhibit a lower and an upper bound for the minimal k such that [x₁,x₂]⋯[x_2k-1,x_2k] is an identity for F_n(\mathfrakN_p) for all n and for all p.

Related

• Relatively free associative algebras of ranks 2 and 3 with Lie nilpotency identity and systems of generators for some T-spaces
• Almost Lie nilpotent varieties of associative algebras
• Tensor products of Lie nilpotent associative algebras and applications to codimension sequences
• Weak polynomial identities and their applications
• Associative nil-algebras over finite fields