A resolution (minimal model) of the PROP for bialgebras

2002/09/01 by Martin Markl, Markl, Martin
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AT #math.KT

paper · pdf · doi:10.48550/arxiv.math/0209007

LaTeX2e, 31 pages; an example from the last section removed

openalex publication_date 2002/09/01 · arxiv created 2005/01/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with a minimal resolution of the PROP for bialgebras. We prove a theorem about the form of this resolution (Theorem 15) and give, in Section 5, a lot of explicit formulas for the differential. Our minimal model contains all information about the deformation theory of bialgebras and related cohomology. Algebras over this minimal model are strongly homotopy bialgebras, that is, homotopy invariant versions of bialgebras.

Citations

• A Diagonal on the Associahedra
• The CROCs, non-commutative deformations, and (co)associative bialgebras
• On the invertibility of quantization functors

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