The Jordan algebras of a Lie algebra

DOI10.1016/j.jalgebra.2006.02.035zbMath1113.17015OpenAlexW2090727204WikidataQ115351574 ScholiaQ115351574MaRDI QIDQ868859

Antonio Fernández López, Esther García, Miguel Gómez Lozano

Publication date: 26 February 2007

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.02.035

zbMATH Keywords

Lie algebraJordan algebraJordan systemJordan elementLocal algebra

Mathematics Subject Classification ID

Jordan structures associated with other structures (17C50) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60)

Related Items (21)

Abelian Non Jordan-Lie Inner Ideals of the Orthogonal Finite Dimensional Lie Algebras ⋮ An elemental characterization of strong primeness in Lie algebras ⋮ Jordan algebras at Jordan elements of semiprime rings with involution ⋮ The Kostrikin radical and similar radicals of Lie algebras ⋮ Simple, locally finite dimensional Lie algebras in positive characteristic ⋮ Quasi-Jordan Algebras ⋮ Lie algebras with an algebraic adjoint representation revisited ⋮ A Jordan algebra of a Mal'tsev algebra ⋮ A characterization of the Kostrikin radical of a Lie algebra ⋮ On the speciality of Jordan algebras and subquotients of Lie algebras ⋮ A radical for graded Lie algebras ⋮ Strongly prime algebraic Lie PI-algebras ⋮ Principal Filtrations of Lie Algebras ⋮ Algebraic Lie algebras of bounded degree ⋮ Inner ideal structure of nearly Artinian Lie algebras ⋮ Generalized derivations and centroids of ternary Jordan superalgebras ⋮ Jordan supersystems related to Lie superalgebras ⋮ SPLIT DIALGEBRAS, SPLIT QUASI-JORDAN ALGEBRAS AND REGULAR ELEMENTS ⋮ Imbedding Lie Algebras in Strongly Prime Algebras ⋮ Unnamed Item ⋮ Ad-nilpotent elements of skew index in semiprime rings with involution

Cites Work

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• On the socle of a Jordan pair
• Zelmanov's prime theorem for quadratic Jordan algebras
• Jordan pairs
• The Lie inner ideal structure of associative rings
• Local PI theory of Jordan systems
• Finitary simple Lie algebras
• Towards a Goldie theory for Jordan pairs
• A taste of Jordan algebras
• The structure of quadratic Jordan systems of Clifford type
• The local algebras of Jordan systems
• Primitive Jordan pairs and triple systems
• Von Neumann regularity in Jordan triple systems
• Noetherian Banach Jordan pairs
• Properly algebraic and spectrum-finite ideals in Jordan systems
• LIE ALGEBRAS WITHOUT STRONG DEGENERATION
• On the Existence of Ad-Nilpotent Elements
• On Inner Ideals and Ad-Nilpotent Elements of Lie Algebras
• Jordan Rings with Nonzero Socle
• Derivations on Banach-Jordan Pairs
• Inner Ideals in Quadratic Jordan Algebras
• Local and subquotient inheritance of simplicity in Jordan systems

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