33 citations · 90 across the 37 of their papers we have counts for
7 papers · 1 filter
Deformations of semi-direct products
Maria Alejandra Alvarez, Salim Rivière, Nadina Rojas +2
We exhibit in this article a contraction of the direct product Lie algebra of a finite-dimensional complex Lie algebra onto the semi-direct product Lie algebra $g\r…
Representations of crossed modules and other generalized Yetter-Drinfel'd modules
Victoria Lebed, Friedrich Wagemann
The Yang-Baxter equation plays a fundamental role in various areas of mathematics. Its solutions, called braidings, are built, among others, from Yetter-Drinfel'd modules over a Ho…
Structure theory of Rack-Bialgebras
Charles Alexandre, Martin Bordemann, Salim Riviere +1
In this paper we focus on a certain self-distributive multiplication on coalgebras, which leads to so-called rack bialgebra. Inspired by semi-group theory (adapting the Suschkewits…
On the string Lie algebra
Salim Riviere, Friedrich Wagemann
We construct an abelian representative for the crossed module associated to the string Lie algebra. We show how to apply this construction in order to define quasi-invariant tensor…
Racks, Leibniz algebras and Yetter-Drinfel'd modules
Ulrich Kraehmer, Friedrich Wagemann
A Hopf algebra object in Loday and Pirashvili's category of linear maps entails an ordinary Hopf algebra and a Yetter-Drinfel'd module. We equip the latter with a structure of a br…
Crossed modules of racks
Alissa S. Crans, Friedrich Wagemann
We generalize the notion of a crossed module of groups to that of a crossed module of racks. We investigate the relation to categorified racks, namely strict 2-racks, and trunk-lik…
Associative algebra deformations of the Connes-Moscovici's Hopf algebra
Alice Fialowski, Friedrich Wagemann
We compute the second Hochschild cohomology space of Connes-Moscovici's Hopf algebra , giving the infinitesimal deformations (up to equivalence…