Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Malcev Yang-Baxter equation, weighted $\mathcal{O}$-operators on Malcev algebras and post-Malcev algebras
View through CrossRef
The purpose of this paper is to study the $\mathcal{O}$-operators on Malcev algebras and discuss the solutions of Malcev Yang-Baxter equation by $\mathcal{O}$-operators. Furthermore we introduce the notion of weighted $\mathcal{O}$-operators on Malcev algebras, which can be characterized by graphs of the semi-direct product Malcev algebra. Then we introduce a new algebraic structure called post-Malcev algebras. Therefore, post-Malcev algebras can be viewed as the underlying algebraic structures of weighted $\mathcal{O}$-operators on Malcev algebras. A post-Malcev algebra also gives rise to a new Malcev algebra. Post-Malcev algebras are analogues for Malcev algebras of post-Lie algebras and fit into a bigger framework with a close relationship with post-alternative algebras.
Title: Malcev Yang-Baxter equation, weighted $\mathcal{O}$-operators on Malcev algebras and post-Malcev algebras
Description:
The purpose of this paper is to study the $\mathcal{O}$-operators on Malcev algebras and discuss the solutions of Malcev Yang-Baxter equation by $\mathcal{O}$-operators.
Furthermore we introduce the notion of weighted $\mathcal{O}$-operators on Malcev algebras, which can be characterized by graphs of the semi-direct product Malcev algebra.
Then we introduce a new algebraic structure called post-Malcev algebras.
Therefore, post-Malcev algebras can be viewed as the underlying algebraic structures of weighted $\mathcal{O}$-operators on Malcev algebras.
A post-Malcev algebra also gives rise to a new Malcev algebra.
Post-Malcev algebras are analogues for Malcev algebras of post-Lie algebras and fit into a bigger framework with a close relationship with post-alternative algebras.
Related Results
A criterion for smooth weighted blow-downs (with an appendix by Stephen Obinna)
A criterion for smooth weighted blow-downs (with an appendix by Stephen Obinna)
We establish a criterion for determining when a smooth Deligne–Mumford stack is a weighted blow-up. More precisely, given a smooth Deligne–Mumford stack
...
An Algebraic Approach to the Goldbach and Polignac Conjectures
An Algebraic Approach to the Goldbach and Polignac Conjectures
This paper will give both the necessary and sufficient conditions required to find a counter-example to the Goldbach Conjecture by using an algebraic approach where no knowledge of...
Measurement of b-hadron branching fractions for two-body decays into charmless charged hadrons
Measurement of b-hadron branching fractions for two-body decays into charmless charged hadrons
Abstract
Based on data corresponding to an integrated luminosity of 0.37 fb−1 collected by the LHCb experiment in 2011, the following ratios of branching fract...
Universal decomposed Banach spaces
Universal decomposed Banach spaces
AbstractLet$${\mathcal {B}}$$Bbe a class of finite-dimensional Banach spaces. A$${\mathcal {B}}$$B-decomposed Banach spaceis a Banach spaceXendowed with a family$${\mathcal {B}}_X\...
An extension of Herstein's theorem on Banach algebra
An extension of Herstein's theorem on Banach algebra
<abstract><p>Let $ \mathcal{A} $ be a $ (p+q)! $-torsion free semiprime ring. We proved that if $ \mathcal{H}, \mathcal{D} : \mathcal{A}\to \mathcal{A} $ are two additi...
Deformation Maps of Quasi-Twilled Lie Algebras
Deformation Maps of Quasi-Twilled Lie Algebras
In this paper, we provide a unified approach to study the cohomology theories and deformation theories of various types of operators in the category of Lie algebras, including modi...
On the co-annihilating ideal graph of commutative rings
On the co-annihilating ideal graph of commutative rings
In this research article, we consider a commutative ring with unity denoted as
...