Zero divisors in reduction algebras

Details Zero divisors in reduction algebras Zero divisors in reduction algebras

2011-09-30

arxiv.org/abs/1109.6894v1

Mathematics

Rings and Algebras

Scientific paper

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.

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