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| On the First Hochschild Cohomology linebreak of Admissible Algebras |
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Citation： |
Fang LI,Dezhan TAN.On the First Hochschild Cohomology linebreak of Admissible Algebras[J].Chinese Annals of Mathematics B,2015,36(6):1027~1042 |
| Page view： 1079
Net amount： 952 |
Authors： |
Fang LI; Dezhan TAN |
Foundation： |
This work was supported by the National Natural Science Foundation of China
(Nos.\,11271318, 11171296, 11401522, J1210038) and the Specialized Research
Fund for the Doctoral Program of Higher Education of China (No. 20110101110010)
and the Zhejiang Provincial Natural Science Foundation of China (No.\,LZ13A010001). |
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| Abstract： |
The aim of this paper is to investigate the first Hochschild
cohomology of admissible algebras which can be regarded as a
generalization of basic algebras. For this purpose, the authors
study differential operators on an admissible algebra. Firstly,
differential operators from a path algebra to its quotient algebra
as an admissible algebra are 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 $0$. |
Keywords： |
Quiver, Admissible algebra, Differential operators, Cohomology |
Classification： |
16E40, 16G20, 16W25, 17B70 |
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