Notes on Cohomologies of Ternary Algebras of Associative Type

Abstract

The aim of this paper is to investigate the cohomologies for ternary algebras of associative type. We study in particular the cases of partially associative ternary algebras and weak totally associative ternary algebras. Also, we consider the Takhtajan's construction, which was used to construct a cohomology of ternary Nambu-Lie algebras using Chevalley-Eilenberg cohomology of Lie algebras, and discuss it in the case of ternary algebras of associative type. One of the main results of this paper states that a deformation cohomology does not exist for partially associative ternary algebras which implies that their operad is not a Koszul operad.

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Cited by in corpus (4)

• (Non-)Koszulness of operads for n-ary algebras, galgalim and other curiosities
• The n-ary algebra of tensors and of cubic and hypercubic matrices
• (Co)associative $3$-ary (co)algebras and infinitesimal bialgebras: construction and main properties
• Hom-coassociative ternary coalgebras and infinitesimal bialgebras