### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Brian Nakamura**, Rutgers University, bnaka {at} math [dot] rutgers [dot] edu
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Minimal Examples of Non-Koszul A(G)

Speaker: **David Nacin**, William Patterson (visiting Rutgers)

Date: Thursday, December 8, 2011 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

The class of algebras associated to directed graphs discovered by Gelfand, Retakh, Serconek, and Wilson are related to factorizations of polynomials over non-commutative algebras. In 2008 the first non-Koszul example of an algebra of this type was found by mathematicians Cassidy and Sheldon. Recent results by Retakh, Serconek and Wilson have produced conditions for numerical Koszulity based upon the homological properties of the underlying graph. We discuss a computer aided proof which gives the minimal example of a layered graph producing an A(G) which fails to be Koszul. We also discuss the relationship between this algebra, the Cassidy-Sheldon example and other similar non-koszul algebras.

See: http://www.math.rutgers.edu/~bnaka/expmath/