Publications
A dichotomy for integral group rings via higher modular groups as amalgamated products Vrije Universiteit Brussel
We show that U(ZG), the unit group of the integral group ring ZG, either satisfies Kazhdan's property (T) or is, up to commensurability, a non-trivial amalgamated product, in case G is a finite group satisfying some mild conditions. A key step in the proof is the construction of amalgamated decompositions of the elementary group E2(O), where O is an order in rational division algebra, and of certain arithmetic groups Γ. The methods for the ...
New examples of non-Fourier-Mukai functors Vrije Universiteit Brussel
A celebrated result by Orlov states that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is of geometric origin, i.e. it is a Fourier–Mukai functor. In this paper we prove that any smooth projective variety of dimension ≥ 3 equipped with a tilting bundle can serve as the source variety of a non-Fourier–Mukai functor between smooth projective schemes.
Codimension Growth of Lie algebras with a generalized action Vrije Universiteit Brussel
Let F be a field of characteristic 0 and L a finite dimensional Lie F-algebra endowed with a generalized action by an associative algebra H. We investigate the exponential growth rate of the sequence of H-graded codimensions c H n (L) of L which is a measure for the number of non-polynomial H-identities of L. More precisely, we construct an S-graded Lie algebra (with S a semigroup) which has an irrational exponential growth rate (the exact ...
The Frobenius morphism in invariant theory Vrije Universiteit Brussel Hasselt University
A reduction theorem for τ -rigid modules Vrije Universiteit Brussel
We prove a theorem which gives a bijection between the support τ-tilting modules over a given finite-dimensional algebra A and the support τ-tilting modules over A / I, where I is the ideal generated by the intersection of the center of A and the radical of A. This bijection is both explicit and well-behaved. We give various corollaries of this, with a particular focus on blocks of group rings of finite groups. In particular we show that ...
The Tannaka–Krein Formalism and (Re)Presentations of Universal Quantum Groups Vrije Universiteit Brussel
Embeddings of algebras in derived categories of surfaces Vrije Universiteit Brussel University of Antwerp
Semigroup graded algebras and graded PI-exponent Vrije Universiteit Brussel
Let S be a semigroup. We study the structure of graded-simple S-graded algebras A and the exponential rate PIexp S-gr(A):= lim n→∞cnS−gr(A)n of growth of codimensions c n S-gr (A) of their graded polynomial identities. This is of great interest since such algebras can have non-integer PIexp S-gr(A) despite being finite dimensional and associative. In addition, such algebras can have a non-trivial Jacobson radical J(A). All this is in strong ...