Associative algebra deformations of the Connes-Moscovici's Hopf algebra H₁

2008/08/27 by Alice Fialowski, Fialowski, Alice, Friedrich Wagemann +1
Mathematics · #16E40 #16S80 #17B56 #17B65 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.AG #math.QA #msc:16E40 #msc:16S80 #msc:17B56 #msc:17B65

paper · pdf · doi:10.48550/arxiv.0808.3653

14 pages

openalex publication_date 2008/08/27 · arxiv created 2009/04/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the second Hochschild cohomology space HH²(H₁) of Connes-Moscovici's Hopf algebra H₁, giving the infinitesimal deformations (up to equivalence) of the associative structure. HH²(H₁) is shown to be one dimensional, and thus Connes-Moscovici's formal deformation of H₁ using Rankin-Cohen brackets is unique up to equivalence.

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