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Keywords:
Hopf algebra; Lie $H$-pseudoalgebra; universal enveloping algebra; Rota-Baxter $H$-operator; annihilation algebra
Hopf algebra; Lie $H$-pseudoalgebra; universal enveloping algebra; Rota-Baxter $H$-operator; annihilation algebra
Summary:
A Lie conformal algebra $L$ is defined as a $\mathbb {C}[\partial ]$-module ($\partial $ is an indeterminate), endowed with a $\mathbb {C}$-linear map $L\otimes L\rightarrow \mathbb {C}[\lambda ]\otimes L$, $a\otimes b\rightarrow [a_{\lambda }b]$ satisfying axioms similar to those of Lie algebra. Then Bakalov, D'Andrea and Kac introduced the notion of Lie $H$-pseudoalgebras by replacing the above polynomial algebra $\mathbb {C}[\partial ]$ with any cocommutative Hopf algebra $H$. We first classify solvable Lie $H$-pseudoalgebras of rank two. Then we consider the Rota-Baxter $H$-operators on such Lie $H$-pseudoalgebras. Finally, we study the relationship between Rota-Baxter $H$-operators on Lie $H$-pseudoalgebra and Rota-Baxter operators on its annihilation algebra.
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