| Northeastern University Mathematics Department | |
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Maurice Auslander Distinguished Lectures and International Conference * April 23 - 28, 2009 Woods Hole, Massachusetts, USA Speck Auditorium, Rowe Laboratory Building, (formerly Whitman), MBL |
| Edward L. Green (Virgina Tech, Blacksburg, VA) Saturday, April 25, 2009 3:00 - 4:00 pm Resolutions, finite generation of Ext, and generalizations of Koszul |
Abstract: Let K be a field and let R be a not necessarily finite dimensional K-algebra. For most of the talk we will assume that R = R0 &oplus R1 &oplus R2 &oplus ... is positively Z-graded with R0 a semisimple K-algebra, R1 of finite length over R0, and R generated in degrees 0 and 1. The Ext-algebra of R is E(R) = ExtR(R0,R0). The goal of the talk is show some strong relationships between the structure of a minimal graded projective resolution of R0 as an R-module to the ring structure of E(R). For example, how does finite generation of E(R) relate to the structure of a minimal graded projective resolution of R0? Moreover, we show that in some special cases, the close connections between resolutions and Ext-algebras lead to results that relate certain R-modules to certain E(R)-modules. Koszul algebras and Koszul duality is possibly the most well known such relationship. I will very briefly review this and spend the remainder of the talk surveying some generalizations of this, including d-Koszul, 2-d-Koszul, almost Koszul, and T-Koszul. |
Dieter Happel (TU Chemnitz, Germany) Saturday, April 25, 2009 5:00 - 6:00 pm Piecewise hereditary algebras | Abstract: A finite dimensional algebra A over an algebraically closed field k is said to be piecewise hereditary if it is derived equivalent to a hereditary, abelian category. The hereditary categories occuring in this situation are up to derived equivalence either module categories over finite dimensional hereditary algebras or coherent sheaves over weighted projective lines in the sense of Geigle and Lenzing. In this talk we will discuss homological properties of piecewise hereditary algebras. In particluar we will state a homological characterization in terms of the strong global dimension of A, which was obtained in joint work with Dan Zacharia. Also we will discuss special types of Nakayama algebras and give a list when they are piecewise hereditary. In this situation a major tool is played by the Coxeter polynomial associated with the algebra A. |
Coffee and Social before the talks 2:00-3:00 pm |
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