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|Title: ||Multiplicative Structures for Koszul Algebras|
|Authors: ||Buchweitz, Ragnar-Olaf|
Green, Edward L.
|Keywords: ||Multiplicative Structures|
|Issue Date: ||2006|
|Citation: ||2000 Mathematics Subject Classification. Primary: 16S37, 16E40.|
|Abstract: ||Let = kQ/I be a Koszul algebra over a field k, where Q is a finite quiver. An algorithmic method for finding a minimal projective resolution F of the graded simple modules over is given in . This resolution is shown to have a "comultiplicative" structure in , and this is used to find a minimal projective resolution P of over the enveloping algebra e. Using
these results we show that the multiplication in the Hochschild cohomology ring of relative to the resolution P is given as a cup product and also provide a description of this product. This comultiplicative structure also yields the structure constants of the Koszul dual of with respect to a canonical basis over k associated to the resolution F. The natural map from the Hochschild
cohomology to the Koszul dual of is shown to be surjective onto the graded centre of the Koszul dual.|
v1 10 Aug 2005|
|Appears in Collections:||Mathematics|
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