Current algebras, highest weight categories and quivers |
| |
Authors: | Vyjayanthi Chari |
| |
Institution: | Department of Mathematics, University of California, Riverside, CA 92521, USA |
| |
Abstract: | We study the category of graded finite-dimensional representations of the polynomial current algebra associated to a simple Lie algebra. We prove that the category has enough injectives and compute the graded character of the injective envelopes of the simple objects as well as extensions between simple objects. The simple objects in the category are parametrized by the affine weight lattice. We show that with respect to a suitable refinement of the standard ordering on the affine weight lattice the category is highest weight. We compute the Ext quiver of the algebra of endomorphisms of the injective cogenerator of the subcategory associated to an interval closed finite subset of the weight lattice. Finally, we prove that there is a large number of interesting quivers of finite, affine and star-shaped type, as well as tame quasi-hereditary algebras, that arise from our study. |
| |
Keywords: | Current algebra Highest weight category Kirillov-Reshetikhin modules Path algebra |
本文献已被 ScienceDirect 等数据库收录! |
|