Pérez-Izquierdo, J. M.
Published in
São Paulo Journal of Mathematical Sciences

The set of formal power series with coefficients in an associative but noncommutative algebra becomes a loop with the substitution product. We study this loop by describing certain Lie and Sabinin algebras related to it. Some examples of Lie algebras satisfying the standard identities of degrees 5 and 6 appear naturally.

Artemovych, Orest D. Prykarpatski, Anatolij K. Blackmore, Denis L.
Published in
Topological Algebra and its Applications

We study algebraic properties of Poisson brackets on non-associative non-commutative algebras, compatible with their multiplicative structure. Special attention is paid to the Poisson brackets of the Lie-Poisson type, related with the special Lie-structures on the differential-topological torus and brane algebras, generalizing those studied before ...

Camacho, L. M. Khudoyberdiyev, A. Kh. Omirov, B. A.
Published in
Algebras and Representation Theory

In this paper we study subalgebras of complex finite dimensional evolution algebras. We obtain the classification of nilpotent evolution algebras whose any subalgebra is an evolution subalgebra with a basis which can be extended to a natural basis of algebra. Moreover, we formulate three conjectures related to the description of such non-nilpotent ...

Cuenca Mira, José Antonio
Published in
Mediterranean Journal of Mathematics

This paper deals with absolute valued algebras A satisfying x2x=xx2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^2 x= xx^2$$\end{document} for all x∈A\documentclass...

Cuenca Mira, José Antonio
Published in
Bulletin of the Malaysian Mathematical Sciences Society

This paper deals with pairs of nonzero idempotents e and f of a third-power associative absolute valued algebra A satisfying (ef)e=e(fe)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \b...

Savin, Diana
Published in
Advances in Difference Equations

In this paper we determine some properties of Fibonacci octonions. Also, we introduce the generalized Fibonacci-Lucas octonions and we investigate some properties of these elements.

BAI, Ruipu CHENG, Yu LIE, Jiaqian MENG, Wei
Published in
Acta Mathematica Scientia

Rozikov, U.A. Murodov, Sh.N.
Published in
Linear Algebra and Its Applications

Recently Ladra and Rozikov introduced a notion of evolution algebra of a “chicken” population (EACP). The algebra is given by a rectangular matrix of structural constants. In this paper we introduce a notion of chain of evolution algebras of a “chicken” population (CEACP). The sequence of matrices of the structural constants for this CEACP satisfie...

BAI, Ruipu CHENG, Yu LIE, Jiaqian MENG, Wei
Published in
Acta Mathematica Scientia

3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensiona...

Rozikov, U.A. Murodov, Sh.N.
Published in
Linear Algebra and Its Applications