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)$ ...