Hochschild Cohomology of an Algebra Associated with a Circular Quiver |
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Authors: | Takahiko Furuya Katsunori Sanada |
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Institution: | 1. Department of Mathematics , Tokyo University of Science, Shinjuku-ku , Tokyo, Japan furuya@ma.kagu.tus.ac.jp;3. Department of Mathematics , Tokyo University of Science, Shinjuku-ku , Tokyo, Japan |
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Abstract: | In this article we show that an algebra A = K Γ/(f(X s )) has a periodic projective bimodule resolution of period 2, where KΓ is the path algebra of the circular quiver Γ with s vertices and s arrows over a commutative ring K, f(x) is a monic polynomial over K and X is the sum of all arrows in KΓ. Moreover, by means of this projective bimodule resolution, we compute the Hochschild cohomology group of A, and we give a presentation of the Hochschild cohomology ring HH?(A) by the generators and the relations in the case K is a field. |
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Keywords: | Circular quiver Hochschild cohomology Periodic projective bimodule resolution |
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