We propose the notion of q–characters for finite-dimensional representations of quantum affine algebras. It is motivated by our theory of deformed W– algebras.

ABSTRACT Since the lightcone self dual spherical membrane, moving in flat target backgrounds, has a direct correspondence with the SU(∞) Nahm equations and the continuous Toda theory, we construct the quantum/Moyal deformations of the self dual membrane in terms of the q-Moyal star product . The q deformations of the SU(∞) Nahm equations are studied and explicit solutions are given. The continu...

We prove in this paper a noncommutative version of Leray Theorem and then Serre Spectral Theorem for noncommutative Serre fibrations. We prove that for NC Serre fibration there are converging spectral sequences with E2 terms as E2 p,q = HPp(B,A;HPq(A)) =⇒ HPp+q(B) and E 2 p,q = HPp(B,A;Kq(A)) =⇒ Kp+q(B). Introduction The ideas of using spectral sequences to operator algebras was started in [C]....

While the study of quantale-like structures goes back up to the 1930’s (notwithstanding that the term itself was introduced in [2] in connection with certain aspects of C∗-algebras), there has recently been much interest in quantales in a variety of contexts. The most important connection probably is with Girard’s linear logic. In particular, one can enunciate the following slogan: Quantales ar...