Is tame open? No answer so far. One may pose the Tame-Open Conjecture: Tame is open. But how to support it? No effective way to date. In this note, the rank of a wild algebra is introduced. The Wild-Rank Conjecture, which implies the Tame-Open Conjecture, is formulated. The Wild-Rank Conjecture is improved to the BasicWild-Rank Conjecture. A covering criterion on the rank of a basic wild algebr...

We construct certain integral structures for the cores of reduced tame extended affine Lie algebras rank at least 2. One main tools to achieve this is a generalization Chevalley automorphisms in context algebras. As an application, groups type associated adjoint representation are defined over arbitrary fields.

We describe the complete set of pairwise non-isomorphic irreducible modules Sα over the algebra R = k〈x, y〉/(xy − yx − y ), and the rule how they could be glued to indecomposables. Namely, we show that Ext1k(Sα, Sβ) = 0, if α 6= β. Also the set of all representations is described subject to the Jordan normal form of Y . We study then properties of the image algebras in the endomorphism ring. Am...

In this survey we present the criterion for tameness of strongly simply connected algebras due to Brustle, de la Pena and Skowronski. We recall relevant concepts representation theory discuss some applications connections other problems.