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The Chevalley and Costant theorems for Mal’tsev algebras

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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.

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Authors and Affiliations

  1. Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    V. N. Zhelyabin & I. P. Shestakov

  2. San-Paulo University, San-Paulo, Brazil

    I. P. Shestakov

Authors
  1. V. N. Zhelyabin
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  2. I. P. Shestakov
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Correspondence to V. N. Zhelyabin.

Additional information

Supported by FAPESP grant No. 04/08537-4 and by SO RAN grant No. 1.9.

Supported by FAPESP grant Nos. 05/60142-7, 05/60337-2 and by CNPq grant No. 304991/2006-6.

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Translated from Algebra i Logika, Vol. 46, No. 5, pp. 560–584, September–October, 2007.

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Zhelyabin, V.N., Shestakov, I.P. The Chevalley and Costant theorems for Mal’tsev algebras. Algebra Logic 46, 303–317 (2007). https://doi.org/10.1007/s10469-007-0031-1

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  • DOI: https://doi.org/10.1007/s10469-007-0031-1

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