Noncommutative Koszul Algebras from Combinatorial Topology

Details Noncommutative Koszul Algebras from Combinatorial Topology Noncommutative Koszul Algebras from Combinatorial Topology

2008-11-21

arxiv.org/abs/0811.3450v1

J. Reine Angew. Math. 646 (2010) 45-63

Mathematics

Rings and Algebras

22 pages, 1 figure

Scientific paper

10.1515/CRELLE.2010.065

Associated to any uniform finite layered graph Gamma there is a noncommutative graded quadratic algebra A(Gamma) given by a construction due to Gelfand, Retakh, Serconek and Wilson. It is natural to ask when these algebras are Koszul. Unfortunately, a mistake in the literature states that all such algebras are Koszul. That is not the case and the theorem was recently retracted. We analyze the Koszul property of these algebras for two large classes of graphs associated to finite regular CW complexes, X. Our methods are primarily topological. We solve the Koszul problem by introducing new cohomology groups H_X(n,k), generalizing the usual cohomology groups H^n(X). Along with several other results, our methods give a new and primarily topological proof of a result of Serconek and Wilson and of Piontkovski.

Affiliated with

Also associated with

No associations

Rating

Noncommutative Koszul Algebras from Combinatorial Topology does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Noncommutative Koszul Algebras from Combinatorial Topology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Noncommutative Koszul Algebras from Combinatorial Topology will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-162634