A_∞-algebra Structures Associated to K₂-algebras

2010/05/27 by Andrew Conner, Conner, Andrew, Pete Goetz +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1005.5185

openalex publication_date 2010/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The notion of a K₂-algebra was recently introduced by Cassidy and Shelton as a generalization of the notion of a Koszul algebra. The Yoneda algebra of any connected graded algebra admits a canonical A_∞-algebra structure. This structure is trivial if the algebra is Koszul. We study the A_∞-structure on the Yoneda algebra of a K₂-algebra. For each non-negative integer n we prove the existence of a K₂-algebra B and a canonical A_∞-algebra structure on the Yoneda algebra of B such that the higher multiplications m_i are nonzero for all 3 ≤ i ≤ n+3. We also provide examples which show that the K₂ property is not detected by any obvious vanishing patterns among higher multiplications.

Citations

• d-Koszul algebras, 2-d determined algebras and 2-d-Koszul algebras

Related

• A-infinity structures related to bi-Koszul algebras
• A^N_∞-algebras
• Quotients of Koszul algebras and 2-d-determined algebras
• On the multi-Koszul property for connected algebras
• Koszul Equivalences in A_∞-Algebras