We compute the center in the case where q is a root of unity. Main steps are to compute the degree of an associated quasipolynomial algebra and to compute the dimensions of some interesting irreducible modules. 1. Introduction Quantum groups arose from a quantum mechanical problem in statistical mechanics , the quantum Yang-Baxter equation (QYBE). Following Drinfeld 5], a quantum group is the d...

The particles with a scattering matrix R(x) are defined as operators Φi(z) satisfying the relation R j′,i′ i,j (x1/x2)Φi′(x1)Φj′ (x2) = Φi(x2)Φj(x1). The algebra generated by those operators is called a Zamolochikov algebra. We construct a new Hopf algebra by adding half of the FRTS construction of a quantum affine algebra with this R(x). Then we double it to obtain a new Hopf algebra such that...

This thesis presents language extensions to Simit, a language for linear algebra on graphs. Currently, Simit doesn’t efficiently handle lattice graphs (regular grids). This thesis defines a stencil assembly construct to capture linear algebra on these graphs. A prototype compiler with a Halide backend demonstrates that these extensions capture the full structure of linear algebra applications o...

in this paper, applying the concept of generalized a-valued norm on a right h  - module and also the notion of ϕ-homomorphism of finsler modules over c  -algebras we rst improve the denition of the finsler module over h  -algebra and then dene ϕ-morphism of finsler modules over h  -algebras. finally we present some results concerning these new ones.

We compare the K-theory and K-homology of the well known CAR algebra. While the K0 group is infinitely generated, we show that it pairs identically to zero with even Fredholm modules over the algebra. We show further that in fact the even K-homology is trivial, while the odd K-homology group is very large. These results give some insight into the K-homology of AF-algebras. 1. The CAR algebra We...