Results 21 to 30 of about 74,106 (122)
Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras [PDF]
Communications in Mathematics, 2022 A Rota-Baxter Leibniz algebra is a Leibniz algebra $(\mathfrak{g},[~,~]_{\mathfrak{g}})$ equipped with a Rota-Baxter operator $T : \mathfrak{g} \rightarrow \mathfrak{g}$.
B. Mondal, R. Saha
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Twisted Rota-Baxter families and NS-family algebras [PDF]
Journal of Algebra, 2022 Family algebraic structures indexed by a semigroup first appeared in the algebraic aspects of renormalizations in quantum field theory. The concept of the Rota-Baxter family and its relation with (tri)dendriform family algebras have been recently ...
A. Das
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Rota—Baxter groups, skew left braces, and the Yang—Baxter equation [PDF]
Journal of Algebra, 2021 Braces were introduced by W. Rump in 2006 as an algebraic system related to the quantum Yang—Baxter equation. In 2017, L. Guarnieri and L. Vendramin defined for the same purposes a more general notion of a skew left brace. In 2021, L. Guo, H.
V. Bardakov, V. Gubarev
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Deformations and cohomology theory of Rota-Baxter 3-Lie algebras of arbitrary weights [PDF]
Journal of Geometry and Physics, 2022 A bstract . A cohomology theory of Rota-Baxter 3-Lie algebras of arbitrary weights is introduced. Formal deformations, abelian extensions, skeletal Rota-Baxter 3-Lie 2-algebras and crossed modules of Rota-Baxter 3-Lie algebras are interpreted by using ...
Shuang-Jian Guo +3 more
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3-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on 3-Lie algebras [PDF]
Journal of Algebra, 2022 A bstract . In this paper, first we introduce the notions of relative Rota-Baxter operators of nonzero weight on 3-Lie algebras and 3-post-Lie algebras.
Shuai Hou, Yunhe Sheng, Yanqiu Zhou
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Rota-Baxter operators on the polynomial algebras, integration and averaging operators [PDF]
, 2014 The concept of a Rota–Baxter operator is an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota–Baxter operators and integrals in the case of the polynomial algebra k[x] k[x] .
Guo, Li +5 more
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Factorizable Lie Bialgebras, Quadratic Rota–Baxter Lie Algebras and Rota–Baxter Lie Bialgebras [PDF]
Communications in Mathematical Physics, 2021 In this paper, first we introduce the notion of quadratic Rota–Baxter Lie algebras of arbitrary weight, and show that there is a one-to-one correspondence between factorizable Lie bialgebras and quadratic Rota–Baxter Lie algebras of nonzero weight.
H. Lang, Yunhe Sheng
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Ophthalmology (Rochester, Minn.), 2022 OBJECTIVE To apply retinal nerve fiber layer (RNFL) optical texture analysis (ROTA) in eyes with early glaucoma to investigate (1) the pattern of RNFL defects, (2) how often the papillomacular bundle and papillofoveal bundles were involved, and (3) the ...
C. Leung, Philip Yawen Guo, A. Lam
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Lie theory and cohomology of relative Rota–Baxter operators [PDF]
Journal of the London Mathematical Society, 2021 In this paper, we establish a local Lie theory for relative Rota–Baxter operators of weight 1. First we recall the category of relative Rota–Baxter operators of weight 1 on Lie algebras and construct a cohomology theory for them.
Jun Jiang, Yunhe Sheng, Chen-Chang Zhu
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Cohomology and Deformations of Relative Rota–Baxter Operators on Lie-Yamaguti Algebras [PDF]
Mathematics, 2022 In this paper, we establish the cohomology of relative Rota–Baxter operators on Lie-Yamaguti algebras via the Yamaguti cohomology. Then, we use this type of cohomology to characterize deformations of relative Rota–Baxter operators on Lie-Yamaguti ...
Jia Zhao, Yu Qiao
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