Graded and Koszul Categories

Koszul algebras have arisen in many contexts; algebraic geometry, combinatorics, Lie algebras, non-commutative geometry and topology. The aim of this paper and several sequel papers is to show that for any finite dimensional algebra there is always a naturally associated Koszul theory. To obtain this, the notions of Koszul algebras, linear modules and Koszul duality are extended to additive (graded) categories over a field. The main focus of this paper is to provide these generalizations and the necessary preliminaries.

• Type: Journal
• Year: 2010
• Where: ACS
• Authors: Roberto Martínez-Villa, Øyvind Solberg
• Keywords: ACS 2010, Algebras, Distributed And Parallel Computing, Finite Dimensional Algebra, Koszul Algebras