Tame biextensions of derived tame hereditary algebras

On Ringel-hall Algebras of Tame Hereditary Algebras

Subfields of Nondegenerate Tame Semiramified Division Algebras

We show in this article that in many cases the subfields of a nondegenerate tame semiramified division algebra of prime power degree over a Henselian valued field are inertial field extensions of the center [Th. 2.5, Th. 2.12 and Prop. 2.16 ].

Tame Quivers and Affine Enveloping Algebras

Let g be an affine Kac-Moody algebra with symmetric Cartan datum, n be the maximal nilpotent subalgebra of g. By the Hall algebra approach, we construct integral bases of the Z-form of the enveloping algebra U(n). In particular, the representation theory of tame quivers is essentially used in this paper.

Kummer subfields of tame division algebras over Henselian valued fields

By generalizing the method used by Tignol and Amitsur in [TA85], we determine necessary and sufficient conditions for an arbitrary tame central division algebra D over a Henselian valued field E to have Kummer subfields [Corollary 2.11 and Corollary 2.12]. We prove also that if D is a tame semiramified division algebra of prime power degree p over E such that p 6= char(Ē) and rk(ΓD/ΓF ) ≥ 3 [re...

On minimal disjoint degenerations of modules over tame path algebras

For representations of tame quivers the degenerations are controlled by the dimensions of various homomorphism spaces. Furthermore, there is no proper degeneration to an indecomposable. Therefore, up to common direct summands, any minimal degeneration from M to N is induced by a short exact sequence 0 → U → M → V → 0 with indecomposable ends that add up to N . We study these ’building blocs’ of...