Linearity defect and regularity over a Koszul algebra

Authors

  • Kohji Yanagawa

DOI:

https://doi.org/10.7146/math.scand.a-15095

Abstract

Let A=iNAi be a Koszul algebra over a field K=A0, and modA the category of finitely generated graded left A-modules. The linearity defect ldA(M) of MmodA is an invariant defined by Herzog and Iyengar. An exterior algebra E is a Koszul algebra which is the Koszul dual of a polynomial ring. Eisenbud et al. showed that ldE(M)< for all MmodE. Improving this, we show that the Koszul dual A! of a Koszul commutative algebra A satisfies the following.

  • Let MmodA!. If {dimKMiiZ} is bounded, then ldA!(M)<.
  • If A is complete intersection, then regA!(M)< and ldA!(M)< for all MmodA!.
  • If E=y1,,yn is an exterior algebra, then ldE(M)cn!2(n1)! for MmodE with c:=max.

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Published

2009-06-01

How to Cite

Yanagawa, K. (2009). Linearity defect and regularity over a Koszul algebra. MATHEMATICA SCANDINAVICA, 104(2), 205–220. https://doi.org/10.7146/math.scand.a-15095

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Articles