We study the connection between two combinatorial notions associated to a quiver: the
quiver algebra and the path coalgebra. We show that the quiver coalgebra can be recovered …

We formally introduce and study generalized comatrix coalgebras and upper triangular
comatrix coalgebras, which are not only a dualization but also an extension of classical …

We study arbitrary algebras all of whose indecomposable finite dimensional representations
are uniserial, or more generally, comodules over serial coalgebras. We show that the infinite …

We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated
by the problem of constructing toy-models for quantizations of certain configuration spaces …

We consider the pure semisimplicity conjecture in the infinite dimensional case: if in the
category A-lf of locally finite left A-modules over an algebra A every object decomposes as a …

In this paper, we introduce the notion of (*)-serial coalgebras which is a generalization of
serial coalgebras. We investigate the properties of (*)-serial coalgebras and their …

We give a new criterion for the bijectivity of the antipode of a Hopf algebra in terms of the
tensor category of its co-representations. We apply this to prove the bijectivity of the antipode …

We describe the valued Gabriel quiver of a wedge product of coalgebras and study the
category of comodules of a semiprime coalgebra. In particular, we prove that any monomial …

Let H be an arbitrary pointed Hopf algebra of rank one and G the group of group-like
elements of H. In this paper, we give the decomposition of a tensor product of finite …

We study the connection between two combinatorial notions associated to a quiver: the
quiver algebra and the path coalgebra. We show that the quiver coalgebra can be recovered …