A Koszul algebra R is a ℕ-graded K-algebra whose residue field K has a linear free resolution as an R-module. Many papers and lectures have been given on this topic, so here we collect various properties and facts which are related to being a Koszul algebra, and illustrate their mutual implications or counter-examples. In addition we explain how one can investigate computationally these many aspects, some of which would seem to be intrinsically intractable, and we show many examples by using CoCoA-5.
Koszul algebras and computations
BIGATTI, ANNA MARIA;DE NEGRI, EMANUELA
2017-01-01
Abstract
A Koszul algebra R is a ℕ-graded K-algebra whose residue field K has a linear free resolution as an R-module. Many papers and lectures have been given on this topic, so here we collect various properties and facts which are related to being a Koszul algebra, and illustrate their mutual implications or counter-examples. In addition we explain how one can investigate computationally these many aspects, some of which would seem to be intrinsically intractable, and we show many examples by using CoCoA-5.
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