On Koszulity of Twisted Tensor Products

Details On Koszulity of Twisted Tensor Products On Koszulity of Twisted Tensor Products

2010-11-18

arxiv.org/abs/1011.4243v1

Mathematics

K-Theory and Homology

24 pages, 3 eps figures

Scientific paper

Let R be a semisimple ring. A pair (A,C) is called pre-Koszul if A is a connected graded R-ring and C is a compatible connected graded R-coring. To a pre-Koszul pair we associate several complexes and we show that one of them is exact if and only if all other are so. In this case we say that (A,C) is Koszul. We investigate the connection between Koszul pairs and the Koszulity of A and C. We use Koszul pairs to show that the twisted tensor product of two Koszul rings is Koszul.

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