PBW deformations of Koszul algebras over a nonsemisimple ring

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• 作者：Ji-Wei He ; Fred Van Oystaeyen ; Yinhuo Zhang
• 关键词：Generalized Koszul algebra ; PBW deformation ; Bimodule Koszul resolution ; Artin–Schelter Gorenstein algebra
• 刊名：Mathematische Zeitschrift
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：279
• 期：1-2
• 页码：185-210
• 全文大小：433 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1823

文摘

Let \(B\) be a generalized Koszul algebra over a finite dimensional algebra \(S\) . We construct a bimodule Koszul resolution of \(B\) when the projective dimension of \(S_B\) equals two. Using this we prove a Poincaré–Birkhoff–Witt (PBW) type theorem for a deformation of a generalized Koszul algebra. When the projective dimension of \(S_B\) is greater than two, we construct bimodule Koszul resolutions for generalized smash product algebras obtained from braidings between finite dimensional algebras and Koszul algebras, and then prove the PBW type theorem. The results obtained can be applied to standard Koszul Artin–Schelter Gorenstein algebras in the sense of Minamoto and Mori (Adv Math 226:4061-095, 2011).