Some properties of Fox’s derivations for Lie algebras
- Authors: Krasnikov A.F.1
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Affiliations:
- Omsk State University
- Issue: Vol 38, No 1 (2017)
- Pages: 30-37
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198600
- DOI: https://doi.org/10.1134/S1995080217010127
- ID: 198600
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Abstract
Let F be a free sum of Lie algebras Ai(i ∈ I) and a free Lie algebra G with basis {gj|j ∈ J{ and its ideal N has trivial intersection with each summand Ai. Let U(F) be the universal enveloping algebra of F, NU the ideal in U(F) which is generated by N. In this paper we describe an elements v of the algebra F, such that Dl(v) ≡0 mod NU, where l belongs to a subset of I ∪ J and Dk: U(F) → U(F)(k ∈ I ∪ J) are the Fox derivations of the universal enveloping algebra U(F). Using obtained description, we prove a theorems on freedom.
Keywords
About the authors
A. F. Krasnikov
Omsk State University
Author for correspondence.
Email: phomsk@mail.ru
Russian Federation, pr. Mira 55-A, Omsk, 644077