Results 41 to 50 of about 184 (133)

Rota–Baxter operators on BiHom-associative algebras and related structures [PDF]

Colloquium Mathematicum, 2020
The purpose of this paper is to study Rota-Baxter operators for BiHom-associative algebras. Moreover, we introduce and discuss the properties of the notions of BiHom-(tri)dendriform algebra, BiHom-Zinbiel algebra and BiHom-quadri-algebra. We construct the free Rota-Baxter BiHom-associative algebra and present some observations about categories and ...
Liu L., Makhlouf A., Menini C., Panaite F.   +3 more
openaire   +3 more sources

Rota‐Baxter Leibniz Algebras and Their Constructions

Advances in Mathematical Physics, Volume 2018, Issue 1, 2018., 2018
In this paper, we introduce the concept of Rota‐Baxter Leibniz algebras and explore two characterizations of Rota‐Baxter Leibniz algebras. And we construct a number of Rota‐Baxter Leibniz algebras from Leibniz algebras and associative algebras and discover some Rota‐Baxter Leibniz algebras from augmented algebra, bialgebra, and weak Hopf algebra.
Liangyun Zhang, Linhan Li, Huihui Zheng, Francesco Toppan   +3 more
wiley   +1 more source

Rota‐Baxter Operators on 3‐Dimensional Lie Algebras and the Classical R‐Matrices

Advances in Mathematical Physics, Volume 2017, Issue 1, 2017., 2017
Our aim is to classify the Rota‐Baxter operators of weight 0 on the 3‐dimensional Lie algebra whose derived algebra’s dimension is 2. We explicitly determine all Rota‐Baxter operators (of weight zero) on the 3‐dimensional Lie algebras g. Furthermore, we give the corresponding solutions of the classical Yang‐Baxter equation in the 6‐dimensional Lie ...
Linli Wu, Mengping Wang, Yongsheng Cheng, Boris G. Konopelchenko   +3 more
wiley   +1 more source

Cohomology of weighted Rota-Baxter Lie algebras and Rota-Baxter paired operators

, 2021
In this paper, we define representations and cohomology of weighted Rota-Baxter Lie algebras. As applications of cohomology, we study abelian extensions and formal $1$-parameter deformations weighted Rota-Baxter Lie algebras. Finally, we consider weighted Rota-Baxter paired operators that induces a weighted Rota-Baxter Lie algebra and a representation ...
openaire   +2 more sources

Rota-Baxter Operators of Weight Zero on CayleyDickson Algebra with Matrix Images

Известия Иркутского государственного университета: Серия "Математика"
Rota-Baxter operators present a natural generalization of integration by parts formula for the integral operator. We consider Rota-Baxter operators of weight zero on split octonion algebra over a field of characteristic not 2.
A. S. Panasenko
doaj   +1 more source

The Pivotal Role of Phosphorus in a Resilient Water–Energy–Food Security Nexus

Journal of Environmental Quality, Volume 44, Issue 4, Page 1049-1062, July-August 2015., 2015
We make the case that phosphorus (P) is inextricably linked to an increasingly fragile, interconnected, and interdependent nexus of water, energy, and food security and should be managed accordingly. Although there are many other drivers that influence water, energy, and food security, P plays a unique and under‐recognized role within the nexus.
Helen P. Jarvie, Andrew N. Sharpley, Don Flaten, Peter J. A. Kleinman, Alan Jenkins, Tarra Simmons   +5 more
wiley   +1 more source

Some Results on Zinbiel Algebras and Rota–Baxter Operators

Axioms
Rota–Baxter operators (RBOs) play a substantial role in many subfields of mathematics, especially in mathematical physics. In the article, RBOs on Zinbiel algebras (ZAs) and their sub-adjacent algebras are first investigated.
Jizhong Gao, Junna Ni, Jianhua Yu
doaj   +1 more source

Hom‐O‐Operators and Hom‐Yang‐Baxter Equations

Advances in Mathematical Physics, Volume 2015, Issue 1, 2015., 2015
In Hom‐Lie set, we introduce the concept of Hom‐O‐operators and study its relation with classical Hom‐Yang‐Baxter equation, as well as left‐symmetric Hom‐algebras. We construct the corresponding relation between left‐symmetric Hom‐algebras and Hom‐1‐cocycles, which are both related to classical Hom‐Yang‐Baxter equation. Moreover, in Hom‐algebra setting,
Yuanyuan Chen, Liangyun Zhang, Juan C. Marrero   +2 more
wiley   +1 more source

Cohomology and Crossed Modules of Modified Rota–Baxter Pre-Lie Algebras

Mathematics
The goal of the present paper is to provide a cohomology theory and crossed modules of modified Rota–Baxter pre-Lie algebras. We introduce the notion of a modified Rota–Baxter pre-Lie algebra and its bimodule.
Fuyang Zhu, Wen Teng
doaj   +1 more source

Classification of monomial Rota–Baxter operators on k[x] [PDF]

Journal of Algebra and Its Applications, 2016
Rota–Baxter operators were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics. The polynomial algebra [Formula: see text] plays a central role both in analysis and algebra.
openaire   +2 more sources