The center of the Dipper Donkin quantized matrix algebra.
The centre of completed group algebras of pro- groups.
The characteristic variety of a generic foliation
We confirm a conjecture of Bernstein–Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.
The Chu construction.
The Class Number of Hereditary Orders in Non-Eichler Algebras over Global Fuction Fields.
The classical Yang-Baxter equation on alternative algebras: the alternative -bialgebra structure on Cayley-Dickson matrix algebras.
The classification of compact right chain rings.
The closure of radical classes under finite subdirect products
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.