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Zero divisors in reduction algebras

arxiv.org. math. Cornell University, 2011. No. 1109.6894.
Khoroshkin S. M., Огиевецкий О. В.

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.