2018/12/10 by Fatemeh Bagherzadeh, Bagherzadeh, Fatemeh, Murray R. Bremner +1
Mathematics · #16E40 #16S37 #17A42 #18D50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1812.03947
openalex publication_date 2018/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The cup product in the cohomology of algebras over quadratic operads has been\nstudied in the general setting of Koszul duality for operads. We study the cup\nproduct on the cohomology of n-ary totally associative algebras with an\noperation of even (homological) degree. This cup product endows the cohomology\nwith the structure of an n-ary partially associative algebra with an operation\nof even or odd degree depending on the parity of n. In the cases n = 3 and n =\n4, we provide an explicit definition of this cup product and prove its basis\nproperties.\n