On inner product in modular tensor categories II: Inner product on conformal blocks and affine inner product identities

v 1 7 N ov 1 99 6 ON INNER PRODUCT IN MODULAR TENSOR CATEGORIES . II INNER PRODUCT ON CONFORMAL BLOCKS AND AFFINE INNER PRODUCT IDENTITIES

On an Inner Product in Modular Tensor Categories

In this paper we study some properties of tensor categories that arise in 2dimensional conformal and 3-dimensional topological quantum field theory—socalled modular tensor categories. By definition, these categories are braided tensor categories with duality which are semisimple, have a finite number of simple objects and satisfy some non-degeneracy condition. Our main example of such a categor...

On Inner Product on Conformal

This is the second part of the paper (the rst part is published in Journal of AMS 9 1135. In the rst part, we deened for every modular tensor category (MTC) inner products on the spaces of morphisms and proved that the inner product on the space Hom(L X i X i ; U) is modular invariant. Also, we have shown that in the case of the MTC arising from the representations of the quantum group U q sl n...

$C^{*}$-semi-inner product spaces

In this paper, we introduce a generalization of Hilbert $C^*$-modules which are pre-Finsler modules, namely, $C^{*}$-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$-semi-inner product spaces.

Frames in 2-inner Product Spaces

In this paper, we introduce the notion of a frame in a 2- inner product space and give some characterizations. These frames can be considered as a usual frame in a Hilbert space, so they share many useful properties with frames.