An amorphic association scheme has the property that any of its fusion is also an association scheme. In this paper we generalize the property to be amorphic to an arbitrary C-algebra and prove that any amorphic C-algebra is determined up to isomorphism by the multiset of its degrees and an additional integer equal ±1. Moreover, we show that any amorphic C-algebra with rational structure consta...

Recently B. Hartwig and the second author found a presentation for the three-point sl2 loop algebra via generators and relations. To obtain this presentation they defined an algebra ⊠ by generators and relations, and displayed an isomorphism from ⊠ to the three-point sl2 loop algebra. We introduce a quantum analog of ⊠ which we call ⊠q. We define ⊠q via generators and relations. We show how ⊠q ...

The general notion of what is now called Hall algebra or Ringel-Hall algebra is an algebra defined out of a certain type of category, a "finitary abelian category". Finitary abelian categories are, roughly speaking, categories where the notions of exact sequences make sense and such that for any pair of objects A,B in the category in question, we have # Hom(A,B) <∞ and # Ext1(A,B) <∞. The Hall ...

An amorphic association scheme has the property that any of its fusion is also an association scheme. In this paper we generalize the property to be amorphic to an arbitrary C-algebra and prove that any amorphic C-algebra is determined up to isomorphism by the multiset of its degrees and an additional integer equal ±1. Moreover, we show that any amorphic C-algebra with rational structure consta...

We show that the Nakayama automorphism of a Frobenius algebra R over a field k is independent of the field (Theorem 4). Consequently, the k-dual functor on left R-modules and the bimodule isomorphism type of the k-dual of R, and hence the question of whether R is a symmetric k-algebra, are independent of k. We give a purely ring-theoretic condition that is necessary and sufficient for a finite-...

We produce a complete list of Uq (sl2)-module algebra structures on the quantum plane. The (uncountable family of) isomorphism classes of such structures are described. The composition series of representations in question are presented.

Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C *-algebra of G is an isomorphism.

In this paper, we determine the isomorphism classes of the central simple Poisson algebras introduced earlier by the second author. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.

the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...

We construct solutions to Sklyanin's reeection equation in the case in which the bulk Yang-Baxter solution is of Hecke algebra type. Each solution constitutes an extension of the Hecke algebra together with a spectral parameter dependent boundary operator, K(). We solve for the deening relations of the extension, and for the spectral parameter dependence of the boundary operator. Finding concre...