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Universal envelopes of Malcev Algebras: Pointed Moufang bialgebras

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Abstract

Under study are the pointed unital coassociative cocommutative Moufang H-bialgebras. We prove an analog of the Cartier-Kostant-Milnor-Moore theorem for weakly associative Moufang H-bialgebras. If the primitive elements commute with group-like elements then these Moufang H-bialgebras are isomorphic to the tensor product of a universal enveloping algebra of a Malcev algebra and a loop algebra constructed by a Moufang loop.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    V. N. Zhelyabin

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  1. V. N. Zhelyabin
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Correspondence to V. N. Zhelyabin.

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Original Russian Text Copyright © 2009 Zhelyabin V. N.

The author was supported by the Russian Foundation for Basic Research (Grant 01-09-00157), the FAPESP (05/60142-7), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-344.2008.1), and the Program “Development of the Scientific Potential of Higher School” of the Russian Federal Agency for Education (Grant 2.1.1.419).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 6, pp. 1285–1304, November–December, 2009.

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Zhelyabin, V.N. Universal envelopes of Malcev Algebras: Pointed Moufang bialgebras. Sib Math J 50, 1011–1026 (2009). https://doi.org/10.1007/s11202-009-0112-6

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