Rota–Baxter operators and post-Lie algebra structures on semisimple Lie algebras
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Publication:5227802
DOI10.1080/00927872.2018.1536206zbMath1455.17007arXiv1805.05104OpenAlexW2963652753WikidataQ92485129 ScholiaQ92485129MaRDI QIDQ5227802
Dietrich Burde, Vsevolod Yur'evich Gubarev
Publication date: 7 August 2019
Published in: Communications in Algebra (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1805.05104
Simple, semisimple, reductive (super)algebras (17B20) Yang-Baxter equations (16T25) Lie-admissible algebras (17D25) Yang-Baxter equations and Rota-Baxter operators (17B38)
Related Items
Semisimple decompositions of Lie algebras and prehomogeneous modules ⋮ Rota-Baxter operators on groups ⋮ Unnamed Item ⋮ Rota–Baxter operators on a sum of fields ⋮ Crystallographic actions on Lie groups and post-Lie algebra structures ⋮ Integration and geometrization of Rota-Baxter Lie algebras ⋮ Decompositions of algebras and post-associative algebra structures ⋮ Commutative post-Lie algebra structures on nilpotent Lie algebras and Poisson algebras ⋮ Rigidity results for Lie algebras admitting a post-Lie algebra structure
Cites Work
- Unnamed Item
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- Commutative post-Lie algebra structures on Lie algebras
- Affine actions on Lie groups and post-Lie algebra structures
- Post-Lie algebra structures on pairs of Lie algebras
- An analytic problem whose solution follows from a simple algebraic identity
- What is a classical r-matrix?
- Homology of generalized partition posets
- Post-Lie algebras and isospectral flows
- Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras
- Complete left-invariant affine structures on nilpotent Lie groups
- A note on automorphisms of Lie algebras
- The structure of complete left-symmetric algebras
- Variante d'un théorème de H. Ozeki
- Radical d'une algèbre symétrique à gauche
- Commutative post-Lie algebra structures and linear equations for nilpotent Lie algebras
- Rota-Baxter operators on quadratic algebras
- The Auslander conjecture for NIL-affine crystallographic groups.
- Embedding of dendriform algebras into Rota-Baxter algebras
- Baxter algebras and shuffle products
- Universal enveloping Lie Rota-Baxter algebras of pre-Lie and post-Lie algebras
- Left-symmetric algebras, or pre-Lie algebras in geometry and physics
- On the structure of free Baxter algebras
- Some aspects of Baxter's functional equation
- Complete LR-structures on solvable Lie algebras
- LR-algebras
- Rota-Baxter operators on pre-Lie algebras
- Subalgebras of the rank two semisimple Lie algebras
- Post-Lie algebra structures and generalized derivations of semisimple Lie algebras
- Baxter algebras and combinatorial identities. I
- DECOMPOSITIONS OF REDUCTIVE LIE GROUPS
- AFFINE STRUCTURES ON NILMANIFOLDS
- Solutions of the classical Yang-Baxter equation for simple Lie algebras
