Moufang Loops and Generalized Lie-cartan Theorem *
نویسنده
چکیده
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 scientific activity
منابع مشابه
Moufang 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
متن کاملMoufang symmetry X. Generalized Lie and Maurer-Cartan equations of continuous Moufang transformations
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
متن کاملSteiner loops satisfying Moufang's theorem
A loop satisfies Moufang’s theorem whenever the subloop generated by three associating elements is a group. Moufang loops (loops that satisfy the Moufang identities) satisfy Moufang’s theorem, but it is possible for a loop that is not Moufang to nevertheless satisfy Moufang’s theorem. Steiner loops that are not Moufang loops are known to arise from Steiner triple systems in which some triangle ...
متن کاملar X iv : m at h - ph / 0 30 70 14 v 1 8 J ul 2 00 3
It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras and can be seen as a preliminary step to quantum Moufang loops. 1 Moufang loops It is well known how the Lie algebras are connected with the Lie groups. In the present paper, it is explicitly shown h...
متن کاملMoufang Loops of Small Order
The main result of this paper is the determination of all nonassociative Moufang loops of orders *31. Combinatorial type methods are used to consider a number of cases which lead to the discovery of 13 loops of the type in question and prove that there can be no others. All of the loops found are isomorphic to all of their loop isotopes, are solvable, and satisfy both Lagrange's theorem and Syl...
متن کامل