Bound Quiver Algebra Research Articles

Domestic trivial extensions of simply connected algebras

Let A be a finite-dimensional,basicand connected algebra (associative,with 1) over an algebraicallyclosedfield.Itis called simply connected ititis triangular and, for any presentation of A as a bound quiver algebra, the fundamental group of itsbound quiver is trivial. Let T(A) denote thetrivialextension of A by its minimal injective cogenerator. We show that,if A is simply con- nected, then the following conditions are equivalent: (i)T{A) is representation-infiniteand domestic, (ii)T(A) is 2-parametric, (iii) there exists a representation-infinitetiltedalgebra B of Euclidean type Dn or Ep such that T(A)2^T(B), (iv)A is an iterated tilted algebra of type Dn or Ev.