2005/10/11 by Dennis Borisov, Dennis V. Borisov, Borisov, Dennis V.
Mathematics · #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
paper · pdf · doi:10.48550/arxiv.math/0510210
24 pages
arxiv created 2005/10/11 · openalex publication_date 2005/10/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
G_∞-structure is shown to exist on the deformation complex of a morphism of associative algebras. The main step of the construction is extension of a B_∞-algebra by an associative algebra. Actions of B_∞-algebras on associative and B_∞-algebras are analyzed, extensions of B_∞-algebras by associative and B_∞-algebras, that they act upon, are constructed. The resulting G_∞-algebra on the deformation complex of a morphism is shown to be quasi-isomorphic to the G_∞-algebra on deformation complex of the corresponding diagram algebra.