Quantum Groups, Quantum Categories and Quantum Field Theory

Zero Modes’ Fusion Ring and Braid Group Representations for the Extended Chiral su(2) WZNW Model

“…Remark 3.1 The content of the right hand side of (3.61) can be already anticipated by interpreting the results of [30,12] about the tensor product expansion of two irreducible V p (i.e., for 1 ≤ p ≤ h ) "from the GR point of view", or by taking into account the well known fact that a relation analogous to (3.61) holds (again for tensor products but this time without restriction on p ) for q generic when all the representations V p are irreducible; in the GR context, one can expect it to remain true after specializing q to a root of unity as well.…”

“…It has been argued at an early stage that the quantum group counterpart of an integer level su(n) k WZNW model is the restricted quantum universal enveloping algebra (QUEA) U q sℓ(n) at q an even root of unity that is factored by the relations E h α = 0 = F h α , K 2h i = 1 I for h = k + n (q h = −1) (1.1) (see [12], Chapter 4; after intermediate sporadic applications, see e.g. [15], it was studied more systematically in [8,5]).…”

Quantum matrix algebra for theSU(n) WZNW model

“…Significant later developments in different directions -beyond the scope of the present paper -can be found e.g. in [32,54,13,58]. )…”

An Introduction to Noncommutative Spaces and their Geometries

“…Here, with any two nonnegative integers p, q, the symbol pIM q (C) stands for 51) and one identifies…”

“…We refer to [76] for details and several applications to Yang-Mills models and gravity theories. For Hopf algebras and quantum groups and their applications to Quantum Field Theory we refer to [38,51,58,64,75,86,96]. Twisted (or pseudo) groups have been proposed in [105].…”