A homological approach to representations of algebras II: tame hereditary algebras

On Ringel-hall Algebras of Tame Hereditary Algebras

Integral Bases of Cluster Algebras and Representations of Tame Quivers

In [CK] and [SZ], the authors constructed the bases of cluster algebras of finite types and of type e A1,1, respectively. In this paper, we will deduce Z-bases for cluster algebras of affine types and compare Z-bases with generic variables in [Du2]. Moreover, we give inductive formulas for computing the multiplication between two generalized cluster variables associated to objects in a tube.

INTEGRAL AND GRADED QUASI-HEREDITARY ALGEBRAS, II WITH APPLICATIONS TO REPRESENTATIONS OF GENERALIZED q-SCHUR ALGEBRAS AND ALGEBRAIC GROUPS

We consider a pair (a, A) consisting of a quasi-hereditary algebra A and a (positively) graded subalgebra a. We present conditions which guarantee that the algebra grA obtained by grading A by its radical filtration is quasi-hereditary and Koszul. In such cases, we also show that the standard and costandard modules for A have a structure as graded modules for a. These results are applied to obt...

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...

On the Structure of Tame Graded Basic Hopf Algebras Ii

In continuation of the article [28] we classify all radically graded basic Hopf algebras of tame type over an algebraically closed field of characteristic 0.