Results 71 to 80 of about 2,636,434 (156)

ROTA-BAXTER OPERATORS ON 3-DIMENSIONAL NILPOTENT ASSOCIATIVE ALGEBRAS [PDF]

, 2020
Associative algebras are introduced into mathematics of the 19th century and are still intensively studied. The classification of associative algebras of small dimensions first appeared in the works of Pierce in 1881.
Karimjanova, Hushruyahon M., Aliyeva, Jamila R., Holmirzayeva, Ziyodahon B.   +2 more
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Weighted relative Rota-Baxter operators on Leibniz algebras and Post-Leibniz algebra structures

, 2022
Comments are ...
openaire   +2 more sources

Zinbiel bialgebras, relative Rota-Baxter operators and the related Yang-Baxter equation

Journal of Algebra
In this paper, we first introduce the notion of a Zinbiel bialgebra and show that Zinbiel bialgebras, matched pairs of Zinbiel algebras and Manin triples of Zinbiel algebras are equivalent. Then we study the coboundary Zinbiel bialgebras, which leads to an analogue of the classical Yang-Baxter equation.
openaire   +2 more sources

Rota-Baxter operators on involutive associative algebras

, 2021
In this paper, we consider Rota–Baxter operators on involutive associative algebras. We define cohomology for Rota–Baxter operators on involutive algebras that governs the formal deformation of the operator.
Das Apurba
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Relative Rota-Baxter operators and crossed homomorphisms on Lie 2-groups

A relative Rota-Baxter operator on Lie 2-groups is introduced as a pair of relative Rota-Baxter operators on the underlying Lie groups which is also a Lie groupoid morphism. Such an operator induces a factorization theorem for Lie 2-groups and gives rise to a categorical solution of the Yang-Baxter equation.
Lang, Honglei, Wang, Shining
openaire   +2 more sources

On Rota-Baxter Nijenhuis TD algebra

, 2014
There was a long standing problem of G. C. Rota regarding the classi- fication of all linear operators on associative algebras that satisfy algebraic identities.

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Quasi-triangular, factorizable anti-dendriform bialgebras and relative Rota-Baxter operators

We introduce the notion of quasi-triangular anti-dendriform bialgebras, which can be induced by the solutions of the AD-YBE whose symmetric parts are invariant. A factorizable anti-dendriform bialgebra leads to a factorization of the underlying anti-dendriform algebra. Moreover, relative Rota-Baxter operators with weights are introduced to characterize
Qinxiu Sun, Min Wu
openaire   +2 more sources

Cumulants, free cumulants and half-shuffles. [PDF]

Proc Math Phys Eng Sci, 2015
Ebrahimi-Fard K, Patras F.
europepmc   +1 more source

Yang-Baxter Equations and Relative Rota-Baxter Operators for Left-Alia Algebras Associated to Invariant Theory

Journal of Nonlinear Mathematical Physics
arXiv admin note: text overlap with arXiv:2403 ...
Kang, Chuangchuang, Liu, Guilai, Yu, Shizhuo   +2 more
openaire   +2 more sources

Relative Rota–Baxter operators of weight 0 on groups, pre-groups, braces, the Yang–Baxter equation and T-structures

Annali di Matematica Pura ed Applicata (1923 -)
In this paper, we study relative Rota-Baxter operators of weight $0$ on groups and give various examples. In particular, we propose different approaches to study Rota-Baxter operators of weight $0$ on groups and Lie groups. We establish various explicit relations among relative Rota-Baxter operators of weight $0$ on groups, pre-groups, braces, set ...
Yunnan Li, Yunhe Sheng, Rong Tang
openaire   +2 more sources