7 papers
Rank two Artin-Schelter regular algebras and non commuting derivations
Vincent Beck, César Lecoutre
If and are two derivations of a commutative algebra such that is locally nilpotent, one can endow with a new product whose filtered semiclassical l…
Submodular functions in additive combinatorics problems for group actions and representations
Vincent Beck, Cédric Lecouvey
We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion…
Torsion subgroups of quasi-abelianized braid groups
Vincent Beck, Ivan Marin
This article extends the works of Gonçalves, Guaschi, Ocampo [GGO] and Marin [MAR2] on finite subgroups of the quotients of generalized braid groups by the derived subgroup of thei…
Additive combinatorics methods in associative algebras
Vincent Beck, Cédric Lecouvey
We adapt methods coming from additive combinatorics in groups to the study of linear span in associative unital algebras. In particular, we establish for these algebras analogues o…
Abelianization of Subgroups of Reflection Group and their Braid Group; an Application to Cohomology
Vincent Beck
The final result of this article gives the order of the extension $$\xymatrix{1\ar[r] & P/[P,P] \ar^{j}[r] & B/[P,P] \ar^-{p}[r] & W \ar[r] & 1}$$ as an element of the cohomology g…
Fonctorial Construction of Frobenius Categories
Vincent Beck
Let $\Ascr,\Bscr$ be exact categories with $\Ascr$ karoubian and be an exact functor. Under suitable adjonction hypotheses for , we are able to show that the direct factors…
Exterior Algebra Structure for Relative Invariants of Reflection Groups
Vincent Beck
Let be a reflection group acting on a vector space (over a field with zero characteristic). We denote by the coordinate ring of , by a finite dimensional $G…