Lie tori -- a simple characterization of extended affine Lie algebras

DOI10.2977/prims/1166642158zbMath1148.17017OpenAlexW2010112454MaRDI QIDQ863791

Yoji Yoshii

Publication date: 1 February 2007

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1166642158

zbMATH Keywords

coreextended affine Lie algebraLie torus

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Graded Lie (super)algebras (17B70) Other nonassociative rings and algebras (17D99)

Related Items (28)

Lie Tori and Their Fixed Point Subalgebras ⋮ Classification of level zero irreducible integrable modules for twisted full toroidal Lie algebras ⋮ Integrable modules for twisted toroidal extended affine Lie algebras ⋮ Conjugacy of Cartan subalgebras in EALAs with a non-fgc centreless core ⋮ Hamiltonian extended affine Lie algebra and its representation theory ⋮ Integrable modules for Lie tori ⋮ Chevalley involutions for Lie tori and extended affine Lie algebras ⋮ Structurable tori and extended affine Lie algebras of type BC\(_{1}\). ⋮ On conjugacy of Cartan subalgebras in extended affine Lie algebras ⋮ Central extensions of root graded Lie algebras ⋮ Étale descent of derivations ⋮ Unnamed Item ⋮ Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras – A Survey ⋮ Conjugacy theorems for loop reductive group schemes and Lie algebras ⋮ Locally extended affine Lie algebras ⋮ Integrable modules for graded Lie tori with finite-dimensional weight spaces ⋮ Torsors of isotropic reductive groups over Laurent polynomials ⋮ Locally loop algebras and locally affine Lie algebras ⋮ A new characterization of Kac–Moody–Malcev superalgebras ⋮ Multiloop realization of extended affine Lie algebras and Lie tori ⋮ Integral structures in extended affine Lie algebras ⋮ The Core of a Locally Extended Affine Lie Algebra ⋮ Fixed point subalgebras of root graded Lie algebras ⋮ Invariant bilinear forms of algebras given by faithfully flat descent ⋮ Fgc extended affine Lie algebras as fixed point subalgebras ⋮ Classification of minimal locally affine Lie algebras ⋮ Twisted quantum affinizations and quantization of extended affine lie algebras ⋮ The centroid of extended affine and root graded Lie algebras

Cites Work

• Isotopes of some nonassociative algebras with involution
• A class of nonassociative algebras with involution containing the class of Jordan algebras
• A characterization of affine Kac-Moody Lie algebras
• Structurable tori and extended affine Lie algebras of type BC\(_{1}\).
• Quantum tori and the structure of elliptic quasi-simple Lie algebras
• Derivations and Invariant Forms of Lie Algebras Graded by Finite Root Systems
• Extended affine Lie algebras and their root systems
• Construction of extended affine lie algebras by the twisting process
• Lie algebras graded by the root systems 𝐵𝐶ᵣ,𝑟≥2
• The Alternative Torus and the Structure of Elliptic Quasi-Simple Lie Algebras of Type A 2
• The root system and the core of an extended affine Lie algebra.

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