An easy explicit construction is given for a full and faithful functor from the bounded derived category of modules over an associative algebra A to the stable category of the repetitive algebra of A. This construction simplifies the one given by Happel.
Given a quiver Q, a field K and two (not necessarily admissible) ideals I, I' in the path algebra KQ, we study the problem when the factor algebras KQ/I and KQ/I' of KQ are isomorphic. Sufficient conditions are given in case Q is a tree extension of a cycle.
We give an example of a representation of the Kronecker quiver for which the closure of the corresponding orbit contains a singularity smoothly equivalent to the isolated singularity of two planes crossing at a point. Therefore this orbit closure is neither Cohen-Macaulay nor unibranch.
We extend the theory of spinor class fields and relative spinor class fields to study representation problems in several classical linear algebraic groups over number fields. We apply this theory to study the set of isomorphism classes of maximal orders of central simple algebras containing a given maximal Abelian suborder. We also study isometric embeddings of one skew-Hermitian Quaternionic lattice into another.