# Ternary algebras and calculus of cubic matrices

Banach Center Publications (2011)

- Volume: 93, Issue: 1, page 9-18
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topV. 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.