Notes on cohomologies of ternary algebras of associative type
Ataguema, H. ; Makhlouf, A.
J. Gen. Lie Theory Appl., Tome 3 (2009) no. 3, p. 157-174 / Harvested from Project Euclid
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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 usual deformation cohomology does not exist for partially associative ternary algebras which implies that their operad is not a Koszul operad.
Publié le : 2009-08-15
Classification:  Ternary compositions,  Nonassociative rings,  Algebraic topology,  Homology theories,  Cohomology theories,  17A40,  55N99 
@article{1281106534,
     author = {Ataguema, H. and Makhlouf, A.},
     title = {Notes on cohomologies of ternary algebras of associative type},
     journal = {J. Gen. Lie Theory Appl.},
     volume = {3},
     number = {3},
     year = {2009},
     pages = { 157-174},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1281106534}
}

Ataguema, H.; Makhlouf, A. Notes on cohomologies of ternary algebras of associative type. J. Gen. Lie Theory Appl., Tome 3 (2009) no. 3, pp.  157-174. http://gdmltest.u-ga.fr/item/1281106534/