S. Khoroshkin, O. Ogievetsky. Zero divisors in reduction algebras
Natural Sciences / Mathematics / Algebra
Submitted on: Sep 12, 2012, 17:41:18
Description: We establish the absence of zero divisors in the reduction algebra of a Lie algebra g with respect to its reductive Lie sub-algebra k. The class of reduction algebras include the Lie algebras (they arise when k is trivial) and the Gelfand--Kirillov conjecture extends naturally to the reduction algebras. We formulate the conjecture for the diagonal reduction algebras of sl type and verify it on a simplest example.