The fundamental theorem on representation{{nite quivers in 6] indicates a close connection between the representation type of a quiver and the deeniteness of a certain quadratic form. Later on a… (More)

We use the monomial basis theory developed in [4] to present an elementary algebraic construction of the canonical bases for both the Ringel–Hall algebra of a cyclic quiver and the +-part U of the… (More)

We use the idea of generic extensions to investigate the correspondence between the isomorphism classes of nilpotent representations of a cyclic quiver and the orbits in the corresponding… (More)

By introducing Frobenius morphisms F on algebras A and their modules over the algebraic closure Fq of the finite field Fq of q elements, we establish a relation between the representation theory of A… (More)

We give a systematic description of many monomial bases for a given quantized enveloping algebra and of many integral monomial bases for the associated Lusztig Z[v, v]-form. The relations among… (More)

In the present paper, we introduce the generic extension graph G of a Dynkin or cyclic quiver Q and then compare this graph with the crystal graph C for the quantized enveloping algebra associated to… (More)

Following the work [4], we show that a Frobenius morphism F on an algebra A induces naturally a functor F on the (bounded) derived category D(A) of mod-A, and we further prove that the derived… (More)

We define an explicit action of the quantum loop algebra Uq(ĝln) on the tensor space and show that these actions are compatible with the natural embedding Uq(ĝln) →֒ Uq(ĝln+1). As an application, we… (More)

With each nite directed quiver Q a quasi{hereditary algebra, the so{called twisted double of the path algebra kQ, is associated (This class of algebras contains certain interesting ones).… (More)