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- W88113150 abstract "This is a complex, i.e. the composition of two consecutive maps is zero, and it is known as the Hochschild complex of A. The nth homology group Ker dn/ Im dn+1, denoted HHn(A), is the nth Hochschild homology group of A. The aim of this Research in Teams meeting was to establish a conjecture due to Han for certain classes of algebras. The conjecture, stated in [Han], says that if all the higher Hochschild homology groups of a finite dimensional algebra vanish, then the algebra is of finite global dimension. The motivation for this conjecture was a remark made by Happel in [Hap], a remark which evolved into a cohomological version of the above conjecture, and which became known as “Happel’s question”. However, a counterexample to this cohomological version was found by Buchweitz, Green, Madsen and Solberg in [BGMS]. Han’s conjecture has been establish for some classes of algebras. In [AV-P], Avramov and Vigue-Poirrier showed that it holds for finite dimensional commutative algebras, whereas Solotar and Vigue-Poirrier showed in [SV-P] that it holds for certain classes of finitely generated and graded algebras. We, Bergh and Madsen, established the conjecture for Koszul algebras, local graded algebras and cellular algebras in [BeM], provided the ground field has characteristic zero. Our cooperation began during the workshop “Hochschild Cohomology of Algebras: Structure and Applications”, held at BIRS in September 2007. During this Research in Teams meeting, we studied Hochschild homology basically in two settings. First, we looked at split pairs of algebras, that is, algebras A and B related via a pair" @default.
- W88113150 created "2016-06-24" @default.
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- W88113150 date "2010-01-01" @default.
- W88113150 modified "2023-09-27" @default.
- W88113150 title "HOCHSCHILD HOMOLOGY AND GLOBAL DIMENSION RESEARCH IN TEAMS 22 - 29 NOVEMBER 2009 REPORT" @default.
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