The cocycle equation in division rings.
The coefficient ring of the skew group ring
The Cohomology Ring of a Monomial Algebra.
The cohomology ring of free loop spaces.
The combinatorics of quiver representations
We give a description of faces, of all codimensions, for the cones spanned by the set of weights associated to the rings of semi-invariants of quivers. For a triple flag quiver and its faces of codimension 1 this description reduces to the result of Knutson-Tao-Woodward on the facets of the Klyachko cone. We give new applications to Littlewood-Richardson coefficients, including a product formula for LR-coefficients corresponding to triples of partitions lying on a wall of the Klyachko cone. We systematically...
The completely separating incidence algebras of tame representation type
We prove that a completely separating incidence algebra of a partially ordered set is of tame representation type if and only if the associated Tits integral quadratic form is weakly non-negative.
The component quiver of a self-injective artin algebra
We prove that the component quiver of a connected self-injective artin algebra A of infinite representation type is fully cyclic, that is, every finite set of components of the Auslander-Reiten quiver of A lies on a common oriented cycle in .
The composite of irreducible morphisms in regular components
We study when the composite of n irreducible morphisms between modules in a regular component of the Auslander-Reiten quiver is non-zero and lies in the n+1-th power of the radical ℜ of the module category. We prove that in this case such a composite belongs to . We apply these results to characterize those string algebras having n irreducible morphisms between band modules such that their composite is a non-zero morphism in .
The construction of -solvable Abelian groups
The Construction of Almost Split Sequences, III: Modules Over Two Classes of Tame Local Algebras.
The continuity of Lie homomorphisms
We prove that the separating space of a Lie homomorphism from a Banach algebra onto a Banach algebra is contained in the centre modulo the radical.
The converse of Schur's Lemma in group rings
In this paper, we study the structure of group rings by means of endomorphism rings of their modules. The main tools used here, are the subrings fixed by automorphisms and the converse of Schur's lemma. Some results are obtained on fixed subrings and on primary decomposition of group rings.
The cyclic homology of the group rings.
The derived functors of and protorsion modules
The dimension of a quasi-hereditary algebra
The dimension of the derived category of elliptic curves and tubular weighted projective lines
We show that the dimension of the derived category of an elliptic curve or a tubular weighted projective line is one. We give explicit generators realizing this number, and show that they are in a certain sense minimal.
The Dirac complex on abstract vector variables: megaforms.
The Divisor Class Group of Ordinary and Symbolic Blow-ups.
The duality of Auslander-Reiten quiver of path algebras
Let be a finite union of Dynkin quivers, a finite abelian group, the generalized McKay quiver of and the Auslander-Reiten quiver of . Then acts functorially on the quiver . We show that the Auslander-Reiten quiver of coincides with the generalized McKay quiver of .
The duality theorem for twisted smash products of Hopf algebras and its applications
Let denote the twisted smash product of an arbitrary algebra A and a Hopf algebra H over a field. We present an analogue of the celebrated Blattner-Montgomery duality theorem for , and as an application we establish the relationship between the homological dimensions of and A if H and its dual H* are both semisimple.