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On a Lie Algebraic Approach to Abelian Extensions of Associative Algebras

Part of: Homological methods Modules, bimodules and ideals Rings and algebras with additional structure

Published online by Cambridge University Press:  26 March 2020

Youjun Tan  and
Senrong Xu
Youjun Tan
Affiliation:
College of Mathematics, Sichuan University, Chengdu610064, China e-mail: ytan@scu.edu.cn
Senrong Xu*
Affiliation:
Faculty of Science, Jiangsu University, Zhenjiang 212013, China
*
e-mail: senrongxu@ujs.edu.cn
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Abstract

By using a representation of a Lie algebra on the second Hochschild cohomology group, we construct an obstruction class to extensibility of derivations and a short exact sequence of Wells type for an abelian extension of an associative algebra.

Keywords

Bimodulescohomologiesderivationsabelian extensions

MSC classification

Primary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
Secondary: 16W25: Derivations, actions of Lie algebras 16D20: Bimodules
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 1 , March 2021 , pp. 25 - 38
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

Senrong Xu is the corresponding author.

References

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