On the First Hochschild Cohomology of Admissible Algebras

On the First Hochschild Cohomology of Admissible Algebras

The aim of this paper is to investigate the first Hochschild cohomology of ad- missible algebras which can be regarded as a generalization of basic algebras. For this purpose, the authors study differential operators on an admissible algebra. Firstly, dif- ferential operators from a path algebra to...

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Veröffentlicht in:Chinese annals of mathematics. Serie B 2015-11, Vol.36 (6), p.1027-1042
Hauptverfasser: Li, Fang, Tan, Dezhan
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Sprache:eng
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Applications of Mathematics
Hochschild
Mathematics
Mathematics and Statistics
上同调
代数系数
同调代数
容许
微分算子代数
构造特征
维数公式
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Tan, Dezhan
description The aim of this paper is to investigate the first Hochschild cohomology of ad- missible algebras which can be regarded as a generalization of basic algebras. For this purpose, the authors study differential operators on an admissible algebra. Firstly, dif- ferential operators from a path algebra to its quotient algebra as an admissible algebra ave discussed. Based on this discussion, the first cohomology with admissible algebras as coefficient modules is characterized, including their dimension formula. Besides, for planar quivers, the k-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field k of characteristic 0.
doi_str_mv 10.1007/s11401-015-0919-3
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subjects Applications of Mathematics
Hochschild
Mathematics
Mathematics and Statistics
上同调
代数系数
同调代数
容许
微分算子代数
构造特征
维数公式
title On the First Hochschild Cohomology of Admissible Algebras
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