Construction and Applications of an Additive Basis for the Relatively Free Associative Algebra with the Lie Nilpotency Identity of Degree 5

Сибирский математический журнал

article

S. V. Pchelintsev¹ 

[1] Financial University under the Government of the Russian Federation;Sobolev Institute of Mathematics

关键词: Lie nilpotency identity of degree 5;    additive basis;    central polynomial;    kernel polynomial;    codimension of a T-ideal;   

DOI  :  10.1134/S0037446620010127

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We construct an additive basis for the relatively free associative algebra F(5)(K) with the Lie nilpotency identity of degree 5 over an infinite domain K containing $${1 \over 6}$$. We prove that approximately half of the elements in F(5)(K) are central. We also prove that the additive group of F(5)(ℤ) lacks the elements of simple degree ≥ 5. We find an asymptotic estimation of the codimension of T-ideal, which is generated by the commutator [x1,x2,…,x5] of degree 5.

【 授权许可】

CC BY