Quivers with relations for symmetrizable Cartan matrices
Event details
| Date | 05.05.2015 |
| Hour | 15:15 › 17:00 |
| Speaker | Bernard Leclerc, Université de Caen |
| Location | |
| Category | Conferences - Seminars |
In a joint work with C. Geiss and J. Schröer, we have introduced two classes of algebras associated with pairs (C,D) consisting of a symmetrizable generalized Cartan matrix C and a symmetrizer D (such that DC is symmetric). These algebras, defined by quivers with relations, generalize quiver path algebras and their preprojective algebras (obtained when C is symmetric and D is the unit matrix). I will explain analogues in this setting of classical theorems of Gabriel, Dlab-Ringel, Gelfand-Ponomarev, etc. I will also present a new realization of the positive part of the enveloping algebra of the symmetrizable Kac-Moody algebra defined by C, as a convolution algebra of constructible functions, generalizing a theorem of Schofield and Lusztig.
Practical information
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