The Brauer ring of a commutative ring
The canonical algebras
The category of abelian Hopf algebras
The category of groupoid graded modules
We introduce the abelian category R-gr of groupoid graded modules and give an answer to the following general question: If U: R-gr → R-mod denotes the functor which associates to any graded left R-module M the underlying ungraded structure U(M), when does either of the following two implications hold: (I) M has property X ⇒ U(M) has property X; (II) U(M) has property X ⇒ M has property X? We treat the cases when X is one of the properties: direct summand, free, finitely generated, finitely presented,...
The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences.
The category of partial Doi-Hopf modules and functors
The catenarity of the positive part of the quantized enveloping algebra of a simple Lie algebra of type . (La caténarité de la partie positive de l'algèbre enveloppante quantifiée de l'algèbre de Lie simple de type .)
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...