This article is cited in 1 paper

Universal envelopes of Malcev Algebras: Pointed Moufang bialgebras

V. N. Zhelyabin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

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.

Keywords: Hopf algebra, nonassociative algebra, loop, Lie algebra, Malcev algebra.

UDC: 512.554

Received: 13.10.2008

 English version: Siberian Mathematical Journal, 2009, 50:6, 1011–1026

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