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...

Bai, Ruipu Li, Zhenheng Wang, Weidong
Published in
Frontiers of Mathematics in China

We construct two kinds of infinite-dimensional 3-Lie algebras from a given commutative associative algebra, and show that they are all canonical Nambu 3-Lie algebras. We relate their inner derivation algebras to Witt algebras, and then study the regular representations of these 3-Lie algebras and the natural representations of the inner derivation ...

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.

Zheng, Shanghua Guo, Li
Published in
Frontiers of Mathematics in China

We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence, we obtain free Hom-associative algebras generated by a set under the same conditions for the unary operation.

Bokut, L. A. Chen, Yuqun
Published in
Bulletin of Mathematical Sciences

In this survey we give an exposition of the theory of Gröbner–Shirshov bases for associative algebras, Lie algebras, groups, semigroups, Ω-algebras, operads, etc. We mention some new Composition-Diamond lemmas and applications.

Bai, Ruipu Li, Ying
Published in
Frontiers of Mathematics in China

n-Hom Lie algebras are twisted by n-Lie algebras by means of twisting maps. n-Hom Lie algebras have close relationships with statistical mechanics and mathematical physics. The paper main concerns structures and representations of n-Hom Lie algebras. The concept of nρ-cocycle for an n-Hom Lie algebra (G, [, ...,], α) related to a G-module (V, ρ, β)...