We introduced a non-symmetric tensor product of any two states or any two representations of Cuntz-Krieger algebras associated with a certain non-cocommutative comultiplication in previous our work. In this paper, we show that a certain set of KMS states is closed with respect to the tensor product. From this, we obtain formulae of tensor product of type III factor representations of Cuntz-Krie...

In this paper we study the category C of finite–dimensional representations of affine Lie algebras. The irreducible objects of this category were classified and described explicitly in [2],[4]. It was known however that C was not semisimple. In such a case a natural problem is to describe the blocks of the category. The blocks of an abelian category are themselves abelian subcategories, each of...

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over a field of positive characteristic associated to nontwisted affine Kac-Moody algebras, or rather, to the underlying loop algebras. The main results are the classification of the irreducible modules, a version of Steinberg’s Tensor Product Theorem, and the construction of positive characteristic anal...

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra. The main results are the classification of the irreducible modules, a version of Steinberg’s Tensor Product Theorem, and the construction of positive characte...

If M is both an abelian category and a symmetric monoidal closed category, then it is natural to ask whether projective objects in M are at, and whether the tensor product of two projective objects is projective. In the most familiar such categories, the answer to these questions is obviously yes. However, the category M G of Mackey functors for a compact Lie group G is a category of this type ...

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra. The main results are the classification of the irreducible modules, a version of Steinberg’s Tensor Product Theorem, and the construction of positive characte...

We argue that the notion of identical particles is no longer well defined in quantum systems governed by non-commutative deformations space-time symmetries. Such models are characterized four-momentum space given a non-abelian Lie group. Our analysis based on observation that, for states containing more than one particle, only total momentum system number. obtained from composition individual m...

Novel Lagrangians are discussed in which (non-abelian) electric and magnetic gauge fields appear on a par. To ensure that these Lagrangians describe the correct number of degrees of freedom, tensor gauge fields are included with corresponding gauge symmetries. Non-abelian gauge symmetries that involve both the electric and the magnetic gauge fields can then be realized at the level of a single ...