Identities of the Model Algebra of Multiplicity 2

Сибирский математический журнал

S. V. Pchelintsev¹ 

[1] Financial University Under the Government of the Russian Federation

关键词: free algebra;    proper polynomial;    identity of Lie-nilpotency;    additive basis;    identities of a model algebra;   

DOI  :  10.1134/S0037446618060149

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We construct an additive basis of the free algebra of the variety generated by the model algebra of multiplicity 2 over an infinite field of characteristic not 2 and 3. Using the basis we remove a restriction on the characteristic in the theorem on identities of the model algebra (previously the same was proved in the case of characteristic 0). In particular, we prove that the kernel of the relatively free Lie-nilpotent algebra of index 5 coincides with the ideal of identities of the model algebra of multiplicity 2.

【 授权许可】

CC BY