Ternary algebras and calculus of cubic matrices

V. Abramov, and S. Shitov. "Ternary algebras and calculus of cubic matrices." Banach Center Publications 93.1 (2011): 9-18. <http://eudml.org/doc/282352>.

@article{V2011,
abstract = {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.},
author = {V. Abramov, S. Shitov},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {9-18},
title = {Ternary algebras and calculus of cubic matrices},
url = {http://eudml.org/doc/282352},
volume = {93},
year = {2011},
}

TY - JOUR
AU - V. Abramov
AU - S. Shitov
TI - Ternary algebras and calculus of cubic matrices
JO - Banach Center Publications
PY - 2011
VL - 93
IS - 1
SP - 9
EP - 18
AB - 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.
LA - eng
UR - http://eudml.org/doc/282352
ER -