Ternary algebras and calculus of cubic matrices

• Autorzy: V. Abramov , S. Shitov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 17A40: Ternary compositions
• 16D20: Bimodules

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 93
• Numer: 1
• Strony: 9-18

Daty

wydano

2011

Twórcy

autor

V. Abramov

• Institute of Mathematics, University of Tartu, Liivi 2, Tartu 50409, Estonia

autor

S. Shitov

• Institute of Mathematics, University of Tartu, Liivi 2, Tartu 50409, Estonia

Identyfikatory

DOI

10.4064/bc93-0-1