Hom-Lie structures on Kac-Moody algebras

DOI10.1016/j.jalgebra.2018.08.022zbMath1464.17024arXiv1805.00187OpenAlexW2799001518WikidataQ115350594 ScholiaQ115350594MaRDI QIDQ1794068

Abdenacer Makhlouf, Pasha Zusmanovich

Publication date: 15 October 2018

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.00187

zbMATH Keywords

Jordan algebraaffine Kac-Moody algebrasimple Lie algebra2-cocyclecurrent Lie algebraHom-Lie structure

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Hom-Lie and related algebras (17B61)

Related Items (12)

Regular Hom–Lie structures on strictly upper triangular matrix Lie algebras ⋮ Equivariant one-parameter formal deformations of Hom-Leibniz algebras ⋮ Generalized derivations and Hom-Lie algebra structures on sl2 ⋮ On equivariant Hom-Leibniz cohomology ⋮ Current Hom-Lie algebras ⋮ Regular Hom-Lie structures on Borel subalgebras of finite-dimensional simple Lie algebras ⋮ Regular Hom-Lie structures on incidence algebras ⋮ On α -type (equivariant) cohomology of Hom-pre-Lie algebras ⋮ Transposed Poisson structures ⋮ When Hom-Lie structures form a Jordan algebra ⋮ Matching Hom-setting of Rota-Baxter algebras, dendriform algebras, and pre-Lie algebras ⋮ Ado theorem for nilpotent Hom–Lie algebras

Uses Software

• GAP

Cites Work

• Hom-structures on semi-simple Lie algebras
• Commutative 2-cocycles on Lie algebras
• On automorphisms of Kac-Moody algebras and groups
• Generalized derivations of Lie algebras
• On \(\delta\)-derivations of Lie algebras
• A compendium of Lie structures on tensor products
• Deformations of Lie algebras using \(\sigma\)-derivations
• Hom-Lie algebra structures on semi-simple Lie algebras
• Hom-algebra structures
• Low-dimensional cohomology of current Lie algebras and analogs of the Riemann tensor for loop manifolds
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
• Hom-structures on simple graded Lie algebras of finite growth

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