Biderivations of the higher rank Witt algebra without anti-symmetric condition

Biderivations of the higher rank Witt algebra without anti-symmetric condition

The Witt algebra 𝔚d of rank d(≥ 1) is the derivation algebra of Laurent polynomial algebras in d commuting variables. In this paper, all biderivations of 𝔚d without anti-symmetric condition are determined. As an applications, commutative post-Lie algebra structures on 𝔚d are obtained. Our conclusion...

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Main Authors: Tang Xiaomin, Yang Yu
Format: Article
Language:English
Published: De Gruyter 2018-04-01
Series:Open Mathematics
Subjects:
biderivation
higher rank witt algebra
anti-symmetric
post-lie algebra
17b05
17b40
Online Access:https://doi.org/10.1515/math-2018-0042
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spelling doaj-5621d07c20e34f1f90d2b5514bfa85bd2021-09-06T19:20:10ZengDe GruyterOpen Mathematics2391-54552018-04-0116144745210.1515/math-2018-0042math-2018-0042Biderivations of the higher rank Witt algebra without anti-symmetric conditionTang Xiaomin0Yang Yu1Department of Mathematics, Heilongjiang University, Harbin150080, ChinaDepartment of Mathematics, Heilongjiang University, Harbin150080, ChinaThe Witt algebra 𝔚d of rank d(≥ 1) is the derivation algebra of Laurent polynomial algebras in d commuting variables. In this paper, all biderivations of 𝔚d without anti-symmetric condition are determined. As an applications, commutative post-Lie algebra structures on 𝔚d are obtained. Our conclusions recover and generalize results in the related papers on low rank or anti-symmetric cases.https://doi.org/10.1515/math-2018-0042biderivationhigher rank witt algebraanti-symmetricpost-lie algebra17b0517b40
collection DOAJ
language English
format Article
sources DOAJ
author Tang Xiaomin
Yang Yu
spellingShingle Tang Xiaomin
Yang Yu
Biderivations of the higher rank Witt algebra without anti-symmetric condition
Open Mathematics
biderivation
higher rank witt algebra
anti-symmetric
post-lie algebra
17b05
17b40
author_facet Tang Xiaomin
Yang Yu
author_sort Tang Xiaomin
title Biderivations of the higher rank Witt algebra without anti-symmetric condition
title_short Biderivations of the higher rank Witt algebra without anti-symmetric condition
title_full Biderivations of the higher rank Witt algebra without anti-symmetric condition
title_fullStr Biderivations of the higher rank Witt algebra without anti-symmetric condition
title_full_unstemmed Biderivations of the higher rank Witt algebra without anti-symmetric condition
title_sort biderivations of the higher rank witt algebra without anti-symmetric condition
publisher De Gruyter
series Open Mathematics
issn 2391-5455
publishDate 2018-04-01
description The Witt algebra 𝔚d of rank d(≥ 1) is the derivation algebra of Laurent polynomial algebras in d commuting variables. In this paper, all biderivations of 𝔚d without anti-symmetric condition are determined. As an applications, commutative post-Lie algebra structures on 𝔚d are obtained. Our conclusions recover and generalize results in the related papers on low rank or anti-symmetric cases.
topic biderivation
higher rank witt algebra
anti-symmetric
post-lie algebra
17b05
17b40
url https://doi.org/10.1515/math-2018-0042
work_keys_str_mv AT tangxiaomin biderivationsofthehigherrankwittalgebrawithoutantisymmetriccondition
AT yangyu biderivationsofthehigherrankwittalgebrawithoutantisymmetriccondition
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