Homogeneous averaging operators on simple finite conformal Lie algebras

DOI10.1063/1.4927068zbMath1330.17034arXiv1412.0486OpenAlexW3103026326MaRDI QIDQ5500737

Pavel Sergeevich Kolesnikov

Publication date: 10 August 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.0486

Mathematics Subject Classification ID

Vertex operators; vertex operator algebras and related structures (17B69) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Simple, semisimple, reductive (super)algebras (17B20) Yang-Baxter equations (16T25)

Related Items (7)

Rota–Baxter operators of nonzero weight on the matrix algebra of order three ⋮ Unnamed Item ⋮ Simple finite-dimensional double algebras ⋮ Rota–Baxter operators on a sum of fields ⋮ Conformal classical Yang-Baxter equation, \(S\)-equation and \({\mathcal{O}}\)-operators ⋮ Rota-Baxter operators on quadratic algebras ⋮ Rota-Baxter operators on unital algebras

Cites Work

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• Classification of Lie bialgebras over current algebras
• On the classical Young-Baxter equation for simple Lie algebras
• Averaging algebras, Schröder numbers, rooted trees and operads
• Structure theory of finite conformal algebras
• Embedding of dendriform algebras into Rota-Baxter algebras
• Homogeneous averaging operators on semisimple Lie algebras
• Splitting of Operations, Manin Products, and Rota–Baxter Operators
• Generalizations of the classical Yang-Baxter equation and ${\mathcal O}$O-operators
• Rota-Baxter operators on $\mathrm{sl(2,\mathbb {C})}$ sl (2,C) and solutions of the classical Yang-Baxter equation
• Operads of decorated trees and their duals
• Theory of finite pseudoalgebras

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