Publications
A characterisation of Lie algebras via algebraic exponentiation Vrije Universiteit Brussel
In this article we describe varieties of Lie algebras via algebraic exponentiation, a concept introduced by Gray in his Ph.D. thesis. For K an infinite field of characteristic different from 2, we prove that the variety of Lie algebras over K is the only variety of non-associative K-algebras which is a non-abelian locally algebraically cartesian closed (LACC) category. More generally, a variety of n-algebras V is a non-abelian (LACC) category ...
Some generalizations of preprojective algebras and their properties Hasselt University
Superrigidity of group von Neumann algebras KU Leuven
The PBW property for associative algebras as an integrability condition University of Antwerp
Semigroup graded algebras and codimension growth of graded polynomial identities Vrije Universiteit Brussel
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 ...
Hochschild products and global non-abelian cohomology for algebras. Applications Vrije Universiteit Brussel
Let A be a unital associative algebra over a field k, E a vector space and π:E→A a surjective linear map with V=Ker(π). All algebra structures on E such that π:E→A becomes an algebra map are described and classified by an explicitly constructed global cohomological type object GH 2(A,V). Any such algebra is isomorphic to a Hochschild product A⋆V, an algebra introduced as a generalization of a classical construction. We prove that GH 2(A,V) is ...
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 ...
Unified products for Jordan algebras. Applications Vrije Universiteit Brussel
Given a Jordan algebra A and a vector space V, we describe and classify all Jordan algebras containing A as a subalgebra of codimension dimk(V) in terms of a non-abelian cohomological type object JA(V,A). Any such algebra is isomorphic to a newly introduced object called unified product A♮V. The crossed/twisted product of two Jordan algebras are introduced as special cases of the unified product and the role of the subsequent problem ...