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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/9940

Title: Multiplicative Structures for Koszul Algebras
Authors: Buchweitz, Ragnar-Olaf
Green, Edward L.
Snashall, Nicole
Solberg, Oyvind
Keywords: Multiplicative Structures
Koszul Algebras
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 [9]. This resolution is shown to have a "comultiplicative" structure in [7], 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.
Description: http://arXiv.org/abs/math.RA/0508177 v1 10 Aug 2005
URI: http://hdl.handle.net/1807/9940
Appears in Collections:Mathematics

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