Publicaties
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 ...
Division algebras in linear Gr-categories Universiteit Hasselt
Division algebras in linear Gr-categories Universiteit Antwerpen
The PBW property for associative algebras as an integrability condition Universiteit Antwerpen
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 ...
Semigroup graded algebras and codimension growth of graded polynomial identities Vrije Universiteit Brussel
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 ...
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 ...