Results 11 to 20 of about 3,875,166 (215)

3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie Bialgebras [PDF]

Mathematics, 2022
In this paper, we first introduce the notion of a 3-Hom–Lie bialgebra and give an equivalent description of the 3-Hom–Lie bialgebras, the matched pairs and the Manin triples of 3-Hom–Lie algebras.
Shuangjian Guo, Shengxiang Wang, Xiaohui Zhang   +2 more
doaj   +7 more sources

Left-symmetric algebras, or pre-Lie algebras in geometry and physics [PDF]

Open Mathematics, 2006
Abstract In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and renormalization theory), where the name pre-Lie algebras is used quite often.
Burde Dietrich
doaj   +5 more sources

Commutators of Pre-Lie n-Algebras and PL_∞-Algebras

Mathematics, 2021
We show that a PL∞-algebra V can be described by a nilpotent coderivation of degree −1 on coalgebra P*V. Based on this result, we can generalise the result of Lada to show that every A∞-algebra carries a PL∞-algebra structure and every PL∞-algebra ...
Mengjun Wang, Zhixiang Wu
doaj   +3 more sources

Matching Hom-Setting of Rota-Baxter Algebras, Dendriform Algebras, and Pre-Lie Algebras [PDF]

Advances in Mathematical Physics, 2020
In this paper, we introduce the Hom-algebra setting of the notions of matching Rota-Baxter algebras, matching (tri)dendriform algebras, and matching pre-Lie algebras.
Dan Chen, Xiao-Song Peng, Chia Zargeh, Yi Zhang   +3 more
doaj   +3 more sources

Nijenhuis Operators on 2D Pre-Lie Algebras and 3D Associative Algebras

Axioms
In this paper, we describe all Nijenhuis operators on 2-dimensional complex pre-Lie algebras and 3-dimensional complex associative algebras. As an application, using these operators, we obtain solutions to the classical Yang-Baxter equation on the ...
Xiaoguang Zou, Xiang Gao, Chuangchuang Kang, Jiafeng Lü   +3 more
doaj   +3 more sources

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   +3 more sources

Heisenberg-Lie commutation relations in Banach algebras. [PDF]

, 2009
Given q1, q2 ∈ ℂ { 0 }, we construct a unital Banach algebra Bq1, q2 that contains a universal normalised solution to the (q1, q2)-deformed Heisenberg-Lie commutation relations in the following specific ...
Laustsen, Niels Jakob, Silvestrov, Sergei D.   +1 more
core   +5 more sources

On upper modular subalgebras of a Lie algebra. [PDF]

, 2004
This paper is a further contribution to the extensive study by a number of authors of the subalgebra lattice of a Lie algebra. We give some necessary and some sufficient conditions for a subalgebra to be upper modular.
Bowman, Kevin, Varea, Vicente R., Towers, David A.   +2 more
core   +4 more sources

On Q-Neutrosophic Soft Fields [PDF]

Neutrosophic Sets and Systems, 2020
As an extension of neutrosophic soft sets, Q-neutrosophic soft sets were established to deal with twodimensional indeterminate data. Different hybrid models of fuzzy sets were utilized to different algebraic structures, for example groups, rings, fields
Majdoleen Abu Qamar, Abd Ghafur Ahmad, Nasruddin Hassan   +2 more
doaj   +1 more source

Some remarks on the Akivis algebras and the Pre-Lie algebras [PDF]

Czechoslovak Mathematical Journal, 2011
In this paper, by using the Composition-Diamond lemma for non-associative algebras invented by A. I. Shirshov in 1962, we give Gröbner-Shirshov bases for free Pre-Lie algebras and the universal enveloping non-associative algebra of an Akivis algebra, respectively. As applications, we show I.P. Shestakov's result that any Akivis algebra is linear and D.
Chen, Yuqun, Li, Yu
openaire   +2 more sources