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Article

Rings of Fractions of Reduction Algebras

Khoroshkin S. M., Ogievetsky O.

We establish the absence of zero divisors in the reduction algebra of a Lie algebra {Mathematical expression} with respect to its reductive Lie subalgebra {Mathematical expression}. We identify the field of fractions of the diagonal reduction algebra of {Mathematical expression} with the standard skew field; as a by-product we obtain a two-parametric family of realizations of this diagonal reduction algebra by differential operators. We also present a new proof of the Poincaré-Birkhoff-Witt theorem for reduction algebras.