Spatial noncommutativity is similar and can even be related to the non-Abelian nature of multiple D-branes. But they have so far seemed independent of each other. Reflecting this decoupling, the algebra of matrix valued fields on noncommutative space is thought to be the simple tensor product of constant matrix algebra and the Moyal-Weyl deformation. We propose scenarios in which the two become...

We construct the theory of non-abelian gauge antisymmetric tensor fields, which generalize the standard Yang-MIlls fields and abelian gauge p-forms. The corresponding gauge group acts on the space of inhomogeneous differential forms and it is shown to be a supergroup. We construct the theory of non-abelian gauge antisymmetric tensor fields, which generalize the standard Yang-MIlls fields and ab...

Crossed complexes have longstanding uses, explicit and implicit, in homotopy theory and the cohomology of groups. It is here shown that the category of crossed complexes over groupoids has a symmetric monoidal closed structure in which the internal Hom functor is built from morphisms of crossed complexes, nonabelian chain homotopies between them and similar higher homotopies. The tensor product...

In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex with values in the derived category of Hausdorff topological abelian groups. Furthermore we introduce a smallness condition for LCA groups and show that such groups have a...

Let G be a group. We denote by ν(G) certain extension of the non-abelian tensor square G⊗G G×G. In this paper we prove that derived subgroup ν(G)′ is central product three normal subgroups ν(G), all isomorphic to G⊗G. As consequence, describe structure each term and lower series group ν(G).

We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product H = H ⊗ · · ·⊗H is separable or entangled. We show that the tensor convolution ( φ . . . φ ) : G → H defined for mappings φ : G → H μ on an almost arbitrary locally compact abelian group G, give rise to formulation of an equivalent problem to the separability one.

A two-form formulation for the N = 2 vector-tensor multiplet is constructed using superfield methods in central charge superspace. The N = 2 non-Abelian standard supergauge multiplet in central charge superspace is also discussed, as is with the associated Chern-Simons form. We give the constraints, solve the Bianchi identities and present the action for a theory of the vector-tensor multiplet ...

we study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesx_{i}. we introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by x boxtimesy. we investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...