On the Simplicity of Lie Algebras Associated to Leavitt Algebras

DOI10.1080/00927872.2010.516292zbMath1262.16001arXiv0908.2179OpenAlexW2963791046MaRDI QIDQ2902251

Darren Funk-Neubauer, Gene D. Abrams

Publication date: 17 August 2012

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

Full work available at URL: https://arxiv.org/abs/0908.2179

zbMATH Keywords

free modulessimple Lie algebrasassociated Lie algebrasLeavitt algebrasCohn algebras

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Endomorphism rings; matrix rings (16S50) Infinite-dimensional Lie (super)algebras (17B65) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Infinite-dimensional simple rings (except as in 16Kxx) (16D30) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (7)

Commutator Leavitt path algebras. ⋮ Centers of path algebras, Cohn and Leavitt path algebras ⋮ Simple Lie algebras arising from Leavitt path algebras. ⋮ Directly Finite Modules of 𝔰𝔩₂𝔡 ⋮ Balanced deep matrix algebras. ⋮ Simple Lie algebras arising from Steinberg algebras of Hausdorff ample groupoids ⋮ Lie solvable Leavitt path algebras

Cites Work

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• Deep matrix algebras of finite type.
• Algebras of quotients of path algebras.
• Simple and nearly simple deep matrix algebras
• The module type of homomorphic images
• The Leavitt path algebra of a graph.
• Isomorphisms between Leavitt algebras and their matrix rings
• Finitely Deep Matrices
• Introduction to Lie Algebras and Representation Theory

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