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OPERADIC APPROACH TO COHOMOLOGY OF ASSOCIATIVE TRIPLE AND N-TUPLE SYSTEMS

Part of: Homological methods General nonassociative rings Rings and algebras arising under various constructions Categories with structure

Published online by Cambridge University Press:  14 November 2019

FATEMEH BAGHERZADEH  and
MURRAY BREMNER Open the ORCID record for MURRAY BREMNER [Opens in a new window]
FATEMEH BAGHERZADEH
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, Canada e-mails: bagherzadeh@math.usask.ca, bremner@math.usask.ca
MURRAY BREMNER
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, Canada e-mails: bagherzadeh@math.usask.ca, bremner@math.usask.ca
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Abstract

The cup product in the cohomology of algebras over quadratic operads has been studied in the general setting of Koszul duality for operads. We study the cup product on the cohomology of n-ary totally associative algebras with an operation of even (homological) degree. This cup product endows the cohomology with the structure of an n-ary partially associative algebra with an operation of even or odd degree depending on the parity of n. In the cases n=3 and n=4, we provide an explicit definition of this cup product and prove its basic properties.

MSC classification

Primary: 18D50: Operads
Secondary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 16S37: Quadratic and Koszul algebras 17A42: Other $n$-ary compositions $(n ge 3)$
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Special Issue S1: Workshop on Nonassociative algebras and their applications , December 2020 , pp. S128 - S141
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019

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