A projective bimodule resolution and the Hochschild cohomology for a cluster-tilted algebra of type D4

Takahiko Furuya

doi:10.55937/sut/1360240084

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Home > Journals > SUT J. Math. > Volume 48 > Issue 2 > Article

June 2012 A projective bimodule resolution and the Hochschild cohomology for a cluster-tilted algebra of type

{_4}

Takahiko Furuya

Author Affiliations +

Takahiko Furuya¹
¹Department of Mathematics Tokyo University of Science 1–3 Kagurazaka, Shinjuku-ku, Tokyo, Japan

SUT J. Math. 48(2): 145-169 (June 2012). DOI: 10.55937/sut/1360240084

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Abstract

In this paper we give explicit projective bimodule resolutions for algebras in a class of some special biserial algebras, which contains a cluster-tilted algebra of type ${_4}$ . As a main result we completely determine the dimensions of the Hochschild cohomology groups for these algebras.

Acknowledgements

The author would like to thank Professor Takao Hayami and the referee for their valuable comments and helpful suggestions.

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Takahiko Furuya. "A projective bimodule resolution and the Hochschild cohomology for a cluster-tilted algebra of type ${_4}$ ." SUT J. Math. 48 (2) 145 - 169, June 2012. https://doi.org/10.55937/sut/1360240084