Coordinate algebras of extended affine Lie algebras of type \(A_1\)

DOI10.1006/jabr.2000.8450zbMath0974.17026OpenAlexW2057739778WikidataQ115395758 ScholiaQ115395758MaRDI QIDQ1841820

Yoji Yoshii

Publication date: 13 December 2001

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

Full work available at URL: https://doi.org/10.1006/jabr.2000.8450

zbMATH Keywords

corecentral extensionJordan torusTits-Kantor-Koecher constructionextended affine Lie algebra of type \(A_1\)

Mathematics Subject Classification ID

Infinite-dimensional Lie (super)algebras (17B65) Jordan structures associated with other structures (17C50)

Related Items (29)

Universal central extensions of linear groups over rings of non-commutative Laurent polynomials, associated \(K_1\)-groups and \(K_2\)-groups ⋮ Derivations and invariant forms of Jordan and alternative tori ⋮ A Serre-type theorem for the elliptic Lie algebras with rank \(\geq 2\) ⋮ Gradings on the Albert algebra and on \(\mathfrak{f}_4\) ⋮ Conjugacy of Cartan subalgebras in EALAs with a non-fgc centreless core ⋮ Integrable representations of toroidal Lie algebras co-ordinatized by rational quantum tori ⋮ Chevalley involutions for Lie tori and extended affine Lie algebras ⋮ Vertex algebras and TKK algebras ⋮ Twisted modules for toroidal vertex algebras ⋮ Structurable Tori ⋮ Lie Tori of TypeBC₂and Structurable Quasitori ⋮ Realization of graded-simple algebras as loop algebras ⋮ Structurable tori and extended affine Lie algebras of type BC\(_{1}\). ⋮ On conjugacy of Cartan subalgebras in extended affine Lie algebras ⋮ Vertex algebras and extended affine Lie algebras coordinated by rational quantum tori ⋮ A quantized Tits-Kantor-Koecher algebra ⋮ A quantized Tits-Kantor-Koecher algebra ⋮ Hermitian representations of a TKK algebra ⋮ Localization of highest weight modules of a class of extended affine Lie algebras ⋮ ROOT-GRADED LIE ALGEBRAS WITH COMPATIBLE GRADING ⋮ Irreducible Representations for the Baby Tits–Kantor–Koecher Algebra ⋮ A Generalization of Extended Affine Lie Algebras ⋮ Locally extended affine Lie algebras ⋮ Derivations of multi-loop algebras ⋮ Multiloop realization of extended affine Lie algebras and Lie tori ⋮ Invariant bilinear forms of algebras given by faithfully flat descent ⋮ Classification of division \({\mathbb Z}^n\)-graded alternative algebras. ⋮ Covering algebras. I: Extended affine Lie algebras ⋮ Jordan tori for a torsion free abelian group

Cites Work

• Jordan algebras of degree 3 and the Tits process
• The structure of strongly prime quadratic Jordan algebras
• Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy
• Simple and prime graded Jordan algebras
• Classification and construction of quasisimple Lie algebras
• Quantum tori and the structure of elliptic quasi-simple Lie algebras
• Lie algebras graded by finite root systems and intersection matrix algebras
• An elementary approach to the Serre-Rost invariant of Albert algebras
• Jordan centroids
• Extended affine Lie algebras and their root systems
• The Alternative Torus and the Structure of Elliptic Quasi-Simple Lie Algebras of Type A 2
• Lie Algebras Graded by 3-Graded Root Systems and Jordan Pairs Covered by Grids
• Finite-Dimensional Division Algebras over Fields
• The root system and the core of an extended affine Lie algebra.
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