2019/03/05 by Junwu Tu, Tu, Junwu
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.AG #math.QA
paper · pdf · doi:10.48550/arxiv.1903.02107
7 pages. Reference added. Title changed. Proof of Corollary 2.2 improved. part (A) of Theorem 1.1 was proved by Isamu Iwanari in arXiv:1604.08283
openalex publication_date 2019/03/05 · arxiv created 2019/03/13 · arxiv updated 2019/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be a finite-dimensional smooth unital cyclic A_∞-algebra. Assume furthermore that A satisfies the Hodge-to-de-Rham degeneration property. In this short note, we prove the non-commutative analogue of the Bogomolov-Tian-Todorov theorem: the deformation functor associated with the differential graded Lie algebra of Hochschild cochains of A is smooth. Furthermore, the deformation functor associated with the DGLA of cyclic Hochschild cochains of A is also smooth.