Im, Bokhee Smith, Jonathan D. H.
Published in
Archiv der Mathematik

A comtrans algebra is said to decompose as the Thomas sum of two subalgebras if it is a direct sum at the module level, and if its algebra structure is obtained from the subalgebras and their mutual interactions as a sum of the corresponding split extensions. In this paper, we investigate Thomas sums of comtrans algebras of bilinear forms. General ...

Figula, Á. Strambach, K.
Published in
Acta Mathematica Hungarica

We construct loops which are semidirect products of groups of affinities. As their elements in many cases one may take transversal subspaces of an affine space. In particular we obtain in this manner smooth loops having Lie groups of affine real transformations as the groups generated by left translations, whereas the groups generated by right tran...

Bai, Ruipu Song, Guojie Zhang, Yaozhong
Published in
Frontiers of Mathematics in China

In this paper, we prove the isomorphic criterion theorem for (n+2)-dimensional n-Lie algebras, and give a complete classification of (n + 2)-dimensional n-Lie algebras over an algebraically closed field of characteristic zero.

Bai, Rui Pu Wu, Wan Qing Li, Zhen Heng
Published in
Acta Mathematica Sinica, English Series

We study the structure of a metric n-Lie algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{G}$$\end{document} over the complex field ℂ. Let \documentclas...

Wilczyński, Dariusz M.
Published in
Journal of Pure and Applied Algebra

A topological proof is given that real compositions algebras of finite dimension greater than one are algebraically closed under polynomial equations with a tame tail.

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

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 Liu, Hui Zhang, Meng
Published in
Chinese Annals of Mathematics, Series B

Associative multiplications of cubic matrices are provided. The N3-dimensional 3-Lie algebras are realized by cubic matrices, and structures of the 3-Lie algebras are studied.

Marcos, J. Carlos Rodríguez-Palacios, Ángel Velasco, M. Victoria
Published in
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas

We prove that normed unital complex (possibly non-associative) algebras with no non-zero left topological divisor of zero are isomorphic to the field C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidema...

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)...