
Corentin VienneCatholic University of Louvain | UCLouvain · Institut de Recherche en Mathématique et Physique (IRMP)
Corentin Vienne
Master of Science
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Publications
Publications (5)
We study the categorical-algebraic condition that internal actions are weakly representable (WRA) in the context of varieties of (non-associative) algebras over a field.
Our first aim is to give a complete characterization of action accessible, operadic quadratic varieties of non-associative algebras which satisfy an identity of degree two and to...
In this article, we characterise the operadic variety of commutative associative algebras over a field via a (categorical) condition: the associativity of the so-called cosmash product. This condition, which is closely related to commutator theory, is quite strong: for example, groups do not satisfy it. However, in the case of commutative associati...
Just like group actions are represented by group automorphisms, Lie algebra actions are represented by derivations: up to isomorphism, a split extension of a Lie algebra $B$ by a Lie algebra $X$ corresponds to a Lie algebra morphism $B\to {\mathit {Der}}(X)$ from $B$ to the Lie algebra ${\mathit {Der}}(X)$ of derivations on $X$ . In this article, w...
Just like group actions are represented by group automorphisms, Lie algebra actions are represented by derivations: up to isomorphism, a split extension of a Lie algebra $B$ by a Lie algebra $X$ corresponds to a Lie algebra morphism $B\to \mathit{Der}(X)$ from $B$ to the Lie algebra $\mathit{Der}(X)$ of derivations on $X$. In this article, we study...