We study associative ternary algebras and describe a general approach which allows us to construct various classes of ternary algebras. Applying this approach to a central bimodule with a covariant derivative we construct a ternary algebra whose ternary multiplication is closely related to the curvature of the covariant derivative. We also apply our approach to a bimodule over two associative (binary) algebras in order to construct a ternary algebra which we use to produce a large class of Lie algebras. We study the calculus of cubic matrices and use this calculus to construct a matrix ternary algebra with associativity of second kind.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-1,
author = {V. Abramov and S. Shitov},
title = {Ternary algebras and calculus of cubic matrices},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {9-18},
zbl = {1275.17005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-1}
}
V. Abramov; S. Shitov. Ternary algebras and calculus of cubic matrices. Banach Center Publications, Tome 95 (2011) pp. 9-18. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc93-0-1/