Mathematics – Representation Theory
Scientific paper
2006-12-08
Advances in Mathematics 216 (2007), no. 2, 811--840
Mathematics
Representation Theory
AMSLaTeX, 25 pages
Scientific paper
10.1016/j.aim.2007.06.006
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 parametized by the affine weight lattice. We show that with respect to a suitable refinement of the standard ordering on affine the 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 a interval closed finite subset of the weight lattice. Finally, we prove that there is a large number of interesting quivers of finite, affine and tame type that arise from our study. We also prove that the path algebra of star shaped quivers are the Ext algebra of a suitable subcategory.
Chari Vyjayanthi
Greenstein Jacob
No associations
LandOfFree
Current algebras, highest weight categories and quivers 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 Current algebras, highest weight categories and quivers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Current algebras, highest weight categories and quivers will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-573391