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

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 ...

Concept of a birepresentation for the Moufang loops is elaborated. 2000 MSC: 20N05

The derivative Noether currents generated by continuous Moufang tranformations are constructed and their equal-time commutators are found. The corresponding charge algebra turns out to be a birepresentation of the tangent Mal’ltsev algebra of an analytic Moufang loop.

The derivative Noether currents generated by continuous Moufang tranformations are constructed and their equal-time commutators are found. The corresponding charge algebra turns out to be a birepresentation of the tangent Mal’ltsev algebra of an analytic Moufang loop.

The Noether currents generated by continuous Moufang tranformations are constructed and their equal-time commutators are found. The corresponding charge algebra turns out to be a birepresentation of the tangent Mal’ltsev algebra of an analytic Moufang loop.

Abstract In this paper, we discuss the generalization of finitary 2-representation theory 2-categories to birepresentation bicategories. previous papers on subject, classification simple transitive 2-representations a given 2-category was reduced that for certain subquotients. These reduction results were all formulated as bijections between equivalence classes 2-representations. generalize the...

noindent We have two goals in this paper. First, we investigate and construct cofree coalgebras over $n$-representations of quivers, limits and colimits of $n$-representations of quivers, and limits and colimits of coalgebras in the monoidal categories of $n$-representations of quivers. Second, for any given quivers $mathit{Q}_1$,$mathit{Q}_2$,..., $mathit{Q}_n$, we construct a new quiver $math...