Hochschild (Co)homology of a Class of Nakayama Algebras
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Acta Mathematica Sinica, English Series  2008, Vol. 24 Issue (7): 1097-1106    DOI: 10.1007/s10114-007-6072-5
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Hochschild (Co)homology of a Class of Nakayama Algebras
Yun Ge XU, Dan WANG
Faculty of Mathematics & Computer Science, Hubei University, Wuhan, 430062, P. R. China
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Abstract Let Λ = kQ/I be a finite-dimensional Nakayama algebra, where Q is an Euclidean diagram Ãn for some n with cyclic orientation, and I is an admissible ideal generated by a single monomial relation. In this note we determine explicitly all the Hochschild homology and cohomology groups of Λ based on a detailed description of the Bardzell complex. Moreover, the cyclic homology of Λ can be calculated in the case that the underlying field is of characteristic zero.
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Yun Ge XU
Key wordsNakayama algebra   Hochschild homology   cyclic homology   Hochschild cohomology     
Received: 2006-02-17;
Fund: Supported by National Natural Science Foundation of China (Grant Nos. 10426014 and 10501010)
Cite this article:   
Yun Ge XU,Dan WANG. Hochschild (Co)homology of a Class of Nakayama Algebras[J]. Acta Mathematica Sinica, English Series, 2008, 24(7): 1097-1106.
http://www.actamath.com/Jwk_sxxb_en//EN/10.1007/s10114-007-6072-5      or     http://www.actamath.com/Jwk_sxxb_en//EN/Y2008/V24/I7/1097
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