A universal enveloping algebra for cocommutative rack bialgebras

Ulrich Kraehmer (1) , Friedrich Wagemann (2)

1 TU Dresden - Technische Universität Dresden = Dresden University of Technology
2 LMJL - Laboratoire de Mathématiques Jean Leray

We construct a bialgebra object in the category of linear maps LM from a cocommutative rack bialgebra. The construction does extend to some non-cocommutative rack bialgberas, as is illustrated by a concrete example. As a separate result, we show that the Loday complex with adjoint coefficients embeds into the rack bialgebra deformation complex for the rack bialgebra defined by a Leibniz algebra.

Mots clés: Universal enveloping algebras; algèbres de Leibniz; rack bigèbres; racks

Domaines: Topologie algébrique [math.AT]; Algèbres quantiques [math.QA]

Ulrich Kraehmer, Friedrich Wagemann. A universal enveloping algebra for cocommutative rack bialgebras. 2018. ⟨hal-01888690⟩