<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="script">O</mml:mi></mml:math>-operators and Nijenhuis operators of associative conformal algebras

Yuan, Lamei

doi:10.1016/j.jalgebra.2022.07.003

Cited by 9 publications

(2 citation statements)

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“…We introduced conformal NS-algebras in [50] by analogy with Leroux's NS-algebras [36]. Definition 5.5.…”

Section: Ns-lie Conformal Algebrasmentioning

confidence: 99%

“…In order to study the operator forms of solutions of the conformal classical Yang-Baxter equation, the authors in [24] introduced the notion of relative Rota-Baxter operators on Lie conformal algebras. See [24,38,50] for further details of relative Rota-Baxter operators on Lie and associative conformal algebras. The twisting theory was introduced by Drinfeld in [16] motivated by the study of quasi-Lie bialgebras and quasi-Hopf algebras.…”

Section: Introductionmentioning

confidence: 99%

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Twisting theory, relative Rota-Baxter type operators and L∞-algebras on Lie conformal algebras

Yuan,

Liu

2023

Journal of Algebra

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“…We introduced conformal NS-algebras in [50] by analogy with Leroux's NS-algebras [36]. Definition 5.5.…”

Section: Ns-lie Conformal Algebrasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Twisting theory, relative Rota-Baxter type operators and L∞-algebras on Lie conformal algebras

Yuan,

Liu

2023

Journal of Algebra

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Conformal r-matrix-Nijenhuis structures, symplectic-Nijenhuis structures, and ON-structures

Liu

Zhou

Yuan

2022

Journal of Mathematical Physics

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In this paper, we first study infinitesimal deformations of a Lie conformal algebra and a Lie conformal algebra with a module (called an [Formula: see text] pair), which lead to the notions of the Nijenhuis operator on the Lie conformal algebra and the Nijenhuis structure on the [Formula: see text] pair, respectively. Then, by adding compatibility conditions between Nijenhuis structures and [Formula: see text]-operators, we introduce the notion of an [Formula: see text]-structure on an [Formula: see text] pair and show that an [Formula: see text]-structure gives rise to a hierarchy of pairwise compatible [Formula: see text]-operators. In particular, we show that compatible [Formula: see text]-operators on a Lie conformal algebra can be characterized by Nijenhuis operators on Lie conformal algebras. Finally, we introduce the notions of the conformal r-matrix-Nijenhuis structure and symplectic-Nijenhuis structure on Lie conformal algebras and study their relations.

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