let $a$ be a nite dimensional $k-$algebra and $r$ be a locally bounded category such that $r rightarrow r/g = a$ is a galois covering dened by the action of a torsion-free group of automorphisms of $r$. following [30], we provide criteria on the convex subcategories of a strongly simply connected category r in order to be a cycle- nite category and describe the module category of $a$. we pro...

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.

Let G $G$ be an affine algebraic group defined over a field k $k$ of characteristic 0. We study the derived moduli space -local systems on pointed connected CW complex X $X$ trivialized at basepoint . This is represented by DG scheme R Loc ( , * ) $ \bm{\mathrm{R}}\mathrm{Loc}_G(X,\ast )$ : we call (co)homology structure sheaf representation homology in and denote it HR \mathrm{HR}_\ast (X,G)$ ...