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The centralizer of a 3-dimensional simple subalgebra in the universal enveloping algebra of a 7-dimensional simple Malcev algebra

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Abstract

Under study are the centralizers of 3-dimensional simple Lie subalgebras in the universal enveloping algebra of a 7-dimensional simple Malcev algebra. We find some sets of generators for these centralizers in characteristic not 2 nor 3 and for the subalgebra generated by the centralizer in the central closure of the universal enveloping algebra in characteristic 3. As a corollary of the main theorem we obtain the available description of the center of universal enveloping algebra of a 7-dimensional simple Malcev algebra.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    T. I. Shabalin

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  1. T. I. Shabalin
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Correspondence to T. I. Shabalin.

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Original Russian Text Copyright © 2013 Shabalin T.I.

The author was supported by the Russian Foundation for Basic Research (Grants 11-01-00938-a and 12-01-31194-mol-a) and the Federal Target Program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” for 2009–2013 (State Contract 14.740.11.0346).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 4, pp. 947–958, July–August, 2013.

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Shabalin, T.I. The centralizer of a 3-dimensional simple subalgebra in the universal enveloping algebra of a 7-dimensional simple Malcev algebra. Sib Math J 54, 759–768 (2013). https://doi.org/10.1134/S0037446613040150

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  • DOI: https://doi.org/10.1134/S0037446613040150

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