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The Hochschild cohomology ring of a class of special biserial algebras. (English) Zbl 1266.16006

Summary: We consider a class of self-injective special biserial algebras \(\Lambda_N\) over a field \(K\) and show that the Hochschild cohomology ring of \(\Lambda_N\) is a finitely generated \(K\)-algebra. Moreover, the Hochschild cohomology ring of \(\Lambda_N\) modulo nilpotence is a finitely generated commutative \(K\)-algebra of Krull dimension two. As a consequence the conjecture of N. Snashall and Ø. Solberg, [Proc. Lond. Math. Soc., III. Ser. 88, No. 3, 705-732 (2004; Zbl 1067.16010)], concerning the Hochschild cohomology ring modulo nilpotence, holds for this class of algebras.

MSC:

16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
16G20 Representations of quivers and partially ordered sets
16E05 Syzygies, resolutions, complexes in associative algebras

Citations:

Zbl 1067.16010
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References:

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