Mathematics – Representation Theory
Scientific paper
2005-02-19
Mathematics
Representation Theory
15 pages
Scientific paper
We realize the current algebra of a Kac-Moody algebra as a quotient of a semi-direct product of the Kac-Moody Lie algebra and the free Lie algebra of the Kac-Moody algebra. We use this realization to study the representations of the current alg ebra. In particular we see that every ad-invariant ideal in the symmetric algebra of the Kac-Moody algebra gives rise in a canonical way to a representation of the current algebra. These representations include certain well-known families of representations of the current algebra of a simple Lie algebra. Another family of examples, which are the classical limits of the Kirillov-Reshe tikhin modules, are also obtained explicitly by using a construction of Kostant. Finally we study extensi ons in the category of finite dimensional modules of the current algebra of a simple Lie algebra.
Chari Vyjayanthi
Greenstein Jacob
No associations
LandOfFree
An application of free Lie algebras to current algebras and their representation theory 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 An application of free Lie algebras to current algebras and their representation theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An application of free Lie algebras to current algebras and their representation theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-174108