Author : Qian Lin (Electrical engineer)
Release : 2010
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Modules Over Affine Lie Algebras at Critical Level and Quantum Groups by : Qian Lin (Electrical engineer)
Download or read book Modules Over Affine Lie Algebras at Critical Level and Quantum Groups written by Qian Lin (Electrical engineer). This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: There are two algebras associated to a reductive Lie algebra g: the De Concini- Kac quantum algebra and the Kac-Moody Lie algebra. Recent results show that the principle block of De Concini -Kac quantum algebra at an odd root of unity with (some) fixed central character is equivalent to the core of a certain t-structure on the derived category of coherent sheaves on certain Springer Fiber. Meanwhile, a certain category of representation of Kac-Moody Lie algebra at critical level with (some) fixed central character is also equivalent to a core of certain t-structure on the same triangulated category. Based on several geometric results developed by Bezurkvanikov et al. these two abelian categories turn out to be equivalent. i.e. the two t-structures coincide.