K2 factors of Koszul algebras and applications to face rings

JOURNAL OF ALGEBRA

卷:368

Article

Conner, Andrew¹  Shelton, Brad² 

[1] Wake Forest Univ, Dept Math, Winston Salem, NC 27109 USA

[2] Univ Oregon, Dept Math, Eugene, OR 97401 USA

关键词: K-2 algebra;    Koszul algebra;    Yoneda algebra;    Stanley-Reisner ring;    Face ring;   

DOI  :  10.1016/j.jalgebra.2012.07.004

来源: Elsevier

【 摘 要 】

Generalizing the notion of a Koszul algebra, a graded k-algebra A is K-2 if its Yoneda algebra Ext(A)(k, k) is generated as an algebra in cohomology degrees 1 and 2. We prove a strong theorem about K-2 factor algebras of Koszul algebras and use that theorem to show the Stanley-Reisner face ring of a simplicial complex Delta is K-2 whenever the Alexander dual simplicial complex Delta* is (sequentially) Cohen-Macaulay. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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