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The Chevalley and Costant theorems for Mal'tsev algebras

V. N. Zhelyabin^a, I. P. Shestakov<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Universidade de São Paulo, Instituto de Matemática e Estatística

Abstract: Centers of universal envelopes for Mal'tsev algebras are explored. It is proved that the center of the universal envelope for a finite-dimensional semisimple Mal'tsev algebra over a field of characteristic 0 is a ring of polynomials in a finite number of variables equal to the dimension of its Cartan subalgebra, and that universal enveloping algebra is a free module over its center. Centers of universal enveloping algebras are computed for some Mal'tsev algebras of small dimensions.

Keywords: Lie algebra, Mal'tsev algebra, bialgebra, universal enveloping algebra, primitive elements, center of algebra, Chevalley theorem, Costant theorem.

UDC: 512.554

Received: 12.03.2007

 English version: Algebra and Logic, 2007, 46:5, 303–317

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