Rota-Baxter operators on $\mathrm{Cur}(\mathrm{sl}_2(\mathbb{C}))$
Vsevolod Gubarev, Roman Kozlov
TL;DR
This paper classifies all Rota-Baxter operators on the simple conformal Lie algebra ((sl_2())) and explores their relation to solutions of the conformal classical Yang-Baxter equation, clarifying their origins.
Contribution
It provides a complete classification of Rota-Baxter operators on ((sl_2())) and links them to solutions of the conformal classical Yang-Baxter equation.
Findings
All Rota-Baxter operators on ((sl_2())) are classified.
Identifies which operators originate from solutions to the conformal classical Yang-Baxter equation.
Clarifies the connection between Rota-Baxter operators and the conformal classical Yang-Baxter equation.
Abstract
We classify all Rota-Baxter operators on the simple conformal Lie algebra and clarify which of them arise from the solutions to the conformal classical Yang-Baxter equation due to the connection discovered by Y. Hong and C. Bai in 2020.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Finite Group Theory Research