In this paper, we give a natural braiding on the universal central extension of Lie crossed module with given in category modules. We also construct braided modules, showing that, when one these constructions exists, both them exist and coincide.

We construct a dynamical lattice model based on crossed module of possibly non-abelian finite groups. Its degrees freedom are defined links and plaquettes, while gauge transformations vertices the underlying lattice. specify Hilbert space, define basic observables (including Hamiltonian) initiate a~discussion model's phase diagram. The constructed generalizes, in appropriate limits reduces to, ...

The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative geometry and particle systems with generalized statistics are indicated. PACS. 02. 40. +m Differential geometry in theoretical physics. PACS. 03. 65. Fd Algebr...

Throughout this paper, k is a field, R is an algebra over k, and H is a Hopf algebra over k. We say that R# σ H is the crossed product of R and H if R# σ H becomes an algebra over k by multiplication: (a#h)(b#g) = h,g a(h 1 · b)σ(h 2 , g 1)#h 3 g 2 Let lpd(R M), lid(R M) and lf d(R M) denote the left projective dimension, left injective dimension and left flat dimension of left R-module M, resp...

It is a well-known result of the covering groups that a subgroup G of the fundamental group at the identity of a semilocally simply connected topological group determines a covering morphism of topological groups with characteristic group G . In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We ...

Following the recent work by Chan [4] and Morton and Hadji [7] on the Homflypt polynomials of some generalized Hopf links, we investigate the Kauffman polynomials of generalized Hopf links. By studying the Kauffman skein module of the solid torus S × D, we establish a similar skein map on the Kauffman skein module of S × D which has distinct eigenvalues. Furthermore we are able to calculate the...

We classify the finite dimensional indecomposable sl(m/n)-modules with at least a typical or singly atypical primitive weight. We do this classification not only for weight modules, but also for generalized weight modules. We obtain that such a generalized weight module is simply a module obtained by “linking” sub-quotient modules of generalized Kac-modules. By applying our results to sl(m/1), ...

The universal C*-algebra generated by n projections has been described. As an immediate corollary one obtains structure theorem for a pair of projections and the solution to an associated index problem. This puts the study of a pair of projections in the proper perspective of noncommutative geometry. keyword: Index problem, crossed product, Fredholm module, pair of projections. MSC 46L87.

A computer storage system which is addressed by content rather than location is described. The design has been verified by constructing and successfully operating a three-word module consisti~g of 81 crossed-film cryotrons on a 6-inch by 3-inch substrate.

Let H be a Hopf algebra. Ju and Cai introduced the notion of twisting of an H-module coalgebra. In this note, we study the relationship between twistings, crossed coproducts and Hopf-Galois coextensions. In particular, we show that a twisting of an H-Galois coextension remains H-Galois if the twisting is invertible.