$\mathcal K_2$ factors of Koszul algebras and applications to face rings

Details $\mathcal K_2$ factors of Koszul algebras and applications to face rings $\mathcal K_2$ factors of Koszul algebras and applications to face rings

2011-09-23

arxiv.org/abs/1109.5211v1

Mathematics

Rings and Algebras

Scientific paper

Generalizing the notion of a Koszul algebra, a graded k-algebra A is K2 if its Yoneda algebra is generated as an algebra in cohomology degrees 1 and 2. We prove a strong theorem about K2 factor algebras of Koszul algebras and use that theorem to show the Stanley-Reisner face ring of a simplicial complex is K2 whenever the Alexander dual simplicial complex is (sequentially) Cohen-Macaulay.

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