2012/04/21 by Alexei Davydov, Davydov, Alexei · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.1204.4828
arxiv created 2012/04/21 · openalex publication_date 2012/04/21 · arxiv updated 2012/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the paper we introduce the notion of twisted derivation of a bialgebra. Twisted derivations appear as infinitesimal symmetries of the category of representations. More precisely they are infinitesimal versions of twisted automorphisms of bialgebras. Twisted derivations naturally form a Lie algebra (the tangent algebra of the group of twisted automorphisms). Moreover this Lie algebra fits into a crossed module (tangent to the crossed module of twisted automorphisms). Here we calculate this crossed module for universal enveloping algebras and for the Sweedler's Hopf algebra.