Graded-commutativity of the Yoneda product of Hopf bimodules.
Group graded rings and smash products
Group-Graded Rings and Modules.
Hall algebras, hereditary algebras and quantum groups.
Hochschild homology and cohomology of Generalized Weyl algebras: the quantum case
We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of ‘quantum’ type in all but a few exceptional cases.
Homological properties of some Weyl algebra extensions
How to categorify one-half of quantum 𝔤𝔩(1|2)
We describe a collection of differential graded rings that categorify weight spaces of the positive half of the quantized universal enveloping algebra of the Lie superalgebra 𝔤𝔩(1|2).
Induced modules of strongly group-graded algebras
Various results on the induced representations of group rings are extended to modules over strongly group-graded rings. In particular, a proof of the graded version of Mackey's theorem is given.
Invariants of Lie color algebras acting on graded algebras
We prove a series of "going-up" theorems contrasting the structure of semiprime algebras and their subalgebras of invariants under the actions of Lie color algebras.
Isomorphisms between graded Frobenius algebras constructed from twisted superpotentials
In order to distinguish the connected graded Frobenius algebras determined by different twisted superpotentials, we introduce the nondegeneracy of twisted superpotentials. We give the sufficient and necessary condition for connected graded Frobenius algebras determined by two nondegenerate twisted superpotentials to be isomorphic. As an application, we classify the connected -graded Frobenius algebra of length 3, whose dimension of the degree 1 is 2.
Konstruktion endlicher graduierter assoziativer Algebren
Koszul equivalences in -algebras.
La dimension de Gel'fand-Kirillov
La théorie classique et moderne des fonctions symétriques
Lectures on minimal models
Lower central series, augmentation quotients and homology of groups.
Modules Graded by G-sets.
Modules over regular algebras of dimension 3.
Modules over the 4-dimensional Sklyanin algebra
--coherent rings and Gorenstein graded modules
Let be a graded ring and be an integer. We introduce and study the notions of Gorenstein -FP-gr-injective and Gorenstein -gr-flat modules by using the notion of special finitely presented graded modules. On -gr-coherent rings, we investigate the relationships between Gorenstein -FP-gr-injective and Gorenstein -gr-flat modules. Among other results, we prove that any graded module in -gr (or gr-) admits a Gorenstein -FP-gr-injective (or Gorenstein -gr-flat) cover and preenvelope, respectively....