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arXiv · 1109.5211

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

Andrew Conner·Brad Shelton
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Abstract

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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Andrew Conner, Brad Shelton. 2011-09-23. $\mathcal K_2$ factors of Koszul algebras and applications to face rings. https://arxiv.org/abs/1109.5211

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