Moufang loops and generalized Lie-Cartan theorem
نویسندگان
چکیده
منابع مشابه
Moufang Loops and Generalized Lie-cartan Theorem *
Generalized Lie-Cartan theorem for linear birepresentations of an analytic Moufang loop is considered. The commutation relations of the generators of the birepresentation are found. In particular, the Lie algebra of the multiplication group of the birepresentation is explicitly given. 2000 MSC: 20N05, 17D10, 20G05 Dedicated to Maks A. Akivis on the occasion of his 85th birthday and 65 years of ...
متن کاملMoufang symmetry I. Generalized Lie and Maurer-Cartan equations
The differential equations for a local analytic Moufang loop are established. The commutation relations for the infinitesimal translations of the analytic Moufang are found. These commutation relations can be seen as a (minimal) generalization of the Maurer-Cartan equations. 2000 MSC: 20N05, 17D10
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The differential equations for a continuous birepresentation of a local analytic Moufang loop are established. The commutation relations for the infinitesimal operators of the birepresentation are found. These commutation relations can be seen as a (minimal) generalization of the Maurer-Cartan equations and do not depend on the particular birepresentation. 2000 MSC: 20N05, 17D10
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An extensive study of Moufang loops is given in [2].1 One defect of that study is that it assumes Moufang's associativity theorem [6], the only published proof of which involves a complicated induction. Using pseudo-automorphisms along with recent methods of Kleinfeld and the author [S], we shall give simple noninductive proofs of three associativity theorems, one of which (Theorem 5.1) general...
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In a series of papers from the 1940’s and 1950’s, R.H. Bruck and L.J. Paige developed a provocative line of research detailing the similarities between two important classes of loops: the diassociative A-loops and the Moufang loops ([1]). Though they did not publish any classification theorems, in 1958, Bruck’s colleague, J.M. Osborn, managed to show that diassociative, commutative A-loops are ...
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ژورنال
عنوان ژورنال: Journal of Generalized Lie Theory and Applications
سال: 2008
ISSN: 1736-5279,1736-4337
DOI: 10.4303/jglta/s080104