Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Identities of relatively free algebras of Lie nilpotent associative algebras (2503.22664v2)

Published 28 Mar 2025 in math.RA

Abstract: In this paper, we consider the relatively free algebra of rank $n$, $F_n(\mathfrak{N}p)$, in the variety of Lie nilpotent associative algebras of index $p$, denoted by $\mathfrak{N}_p$, over a field of characteristic zero. We describe an explicit minimal basis for the polynomial identities of $F_n(\mathfrak{N}_p)$ when $p=3$ and $p=4$, for all $n$, except for $F_3(\mathfrak{N}_4)$. In the general case, we exhibit a lower and an upper bound for the minimal $k$ such that $[x_1,x_2]\cdots[x{2k-1},x_{2k}]$ is an identity for $F_n(\mathfrak{N}_p)$ for all $n$ and for all $p$.

Summary

We haven't generated a summary for this paper yet.

X Twitter Logo Streamline Icon: https://streamlinehq.com