Consider a field k of characteristic zero. Let Q = (qij) be a n× n-matrix with the entries qij ∈ k∗ or qij is an indeterminate, satisfying qijqji = qii = 1. The algebra k[Q] is generated by k and q ij , i, j = 1, . . . , n. Denote k(Q) = Fract(k[Q]) and Γ is the subgroup in k(Q) generated by k and the entries of Q. Throughout the paper R is a k-algebra with a unit. Definition 1.1. We say that R...

We introduce an analogue of the q-Schur algebra associated to Coxeter systems of type b A n?1. We give two constructions of this algebra. The rst construction realizes the algebra as a certain endomorphism algebra arising from an aane Hecke algebra of type b A r?1 , where n r. This generalizes the original q-Schur algebra as deened by Dipper and James, and the new algebra contains the ordinary ...

We introduce an analogue of the q-Schur algebra associated to Coxeter systems of type A n−1. We give two constructions of this algebra. The first construction realizes the algebra as a certain endomorphism algebra arising from an affine Hecke algebra of type A r−1 , where n ≥ r. This generalizes the original q-Schur algebra as defined by Dipper and James, and the new algebra contains the ordina...

Let A be a simple separable unital C*-algebra satisfying the UCT, and assume that A has finite decomposition rank. Let Q denote the UHF algebra with K0(Q) = Q. Then A⊗Q can be tracially approximated by unital Elliott-Thomsen algebras, and therefore A ⊗ Z is an ASH algebra (hence classifiable), where Z is the Jiang-Su algebra.

It is well known that the Clifford algebra Cl p,q associated to a nondegenerate quadratic form on R n (n = p + q) is isomorphic to a matrix algebra K(m) or direct sum K(m) ⊕ K(m) of matrix algebras, where K = R, C, H. On the other hand, there are no explicit expressions for these isomorphisms in literature. In this work, we give a method for the explicit construction of these isomorphisms. Let ...