FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 5, PAGES 147-155

The Heisenberg envelope for the Hochschild algebra of a finite-dimensional Lie algebra

Yu. P. Razmyslov
G. A. Pogudin

Abstract

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We consider some kind of Hopf algebra assigned to any finite-dimensional Lie algebra. This algebra was pointed out by Hochschild. We prove several statements on its embeddings into an algebra of formal power series. In particular, we obtain similar results for Lie algebras. More precisely, a Lie algebra can be embedded into a Lie algebra of special derivations with coefficients in rational functions in (quasi)polynomials.

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Last modified: October 18, 2012