Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras – A Survey
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Publication:2999930
DOI10.1007/978-0-8176-4741-4_3zbMath1261.17023arXiv0805.3460OpenAlexW1917745814MaRDI QIDQ2999930
Publication date: 18 May 2011
Published in: Progress in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0805.3460
Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras (17-02)
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Cites Work
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- Fixed point subalgebras of extended affine Lie algebras
- Lie tori of type \(B_2\) and graded-simple Jordan structures covered by a triangle
- Prime Jordan algebras. II
- Kähler differentials and coverings of complex simple Lie algebras extended over a commutative algebra
- The centroid of extended affine and root graded Lie algebras
- Lie tori -- a simple characterization of extended affine Lie algebras
- Universal coverings of Steinberg Lie algebras of small characteristic
- The Abelianizations of Weyl groups of root systems extended by Abelian groups
- Extended affine root systems. I: Coxeter transformations
- The structure of strongly prime quadratic Jordan algebras
- Derivations and central extensions of finitely generated graded Lie algebras
- The arithmetic theory of loop groups
- Central extensions of Lie algebras
- Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy
- Generators and relations for 3-graded Lie algebras
- Prime nonassociative algebras
- The degeneracy of extended affine Lie algebras
- Vertex representations for \(n\)-toroidal Lie algebras and a generalization of the Virasoro algebra
- A characterization of affine Kac-Moody Lie algebras
- Quadratic Jordan superpairs covered by grids.
- A taste of Jordan algebras
- Globally maximal arithmetic groups.
- Covering algebras. I: Extended affine Lie algebras
- Classification and construction of quasisimple Lie algebras
- The structure of locally finite split Lie algebras
- Affine Kac-Moody algebras graded by affine root systems
- Classification of division \({\mathbb Z}^n\)-graded alternative algebras.
- Steinberg unitary Lie algebras and skew-dihedral homology
- Quantum tori and the structure of elliptic quasi-simple Lie algebras
- Lie algebras graded by finite root systems and intersection matrix algebras
- Simple Lie algebras graded by a root system and \(C\)-admissible subalgebras
- Integrable roots in split graded Lie algebras
- Central extensions of Lie algebras graded by finite root systems
- Infinitesimally central extensions of Chevalley groups
- Iterated loop algebras
- Galois cohomology and forms of algebras over Laurent polynomial rings
- Isotriviality and étale cohomology of Laurent polynomial rings
- Locally extended affine Lie algebras
- Locally finite simple weight modules over twisted generalized Weyl algebras.
- Spiegelungsräume und homogene symmetrische Räume
- Determination of the differentiably simple rings with a minimal ideal
- Systèmes de racines sur un anneau commutatif totalement ordonné. (Root systems over a totally ordered commutative ring)
- The classification of locally finite split simple Lie algebras
- Alternative quasialgebras
- ROOT-GRADED LIE ALGEBRAS WITH COMPATIBLE GRADING
- Isotopy for Extended Affine Lie Algebras and Lie Tori
- Locally extended affine root systems
- Reflection systems and partial root systems
- Multiloop realization of extended affine Lie algebras and Lie tori
- On the Classification of Rational Quantum Tori and the Structure of Their Automorphism Groups
- LIE G-TORI OF SYMPLECTIC TYPE
- Realization of graded-simple algebras as loop algebras
- Derivations and Automorphisms of Nonassociative Matrix Algebras
- Imbedding of Jordan Algebras Into Lie Algebras. II
- Derivations and Invariant Forms of Lie Algebras Graded by Finite Root Systems
- Extended affine Lie algebras and their root systems
- Nonreduced extended affine root systems of nullity 3
- Tits-Kantor-Koecher Superalgebras of Jordan Superpairs Covered by Grids
- Construction of extended affine lie algebras by the twisting process
- Lie algebras graded by the root systems 𝐵𝐶ᵣ,𝑟≥2
- Derivations and invariant forms of Jordan and alternative tori
- Classification of Quantum Tori with Involution
- Locally finite root systems
- Covering algebras II: Isomorphism of loop algebras
- 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
- Derivations of multi-loop algebras
- Generalized Reductive Lie Algebras: Connections With Extended Affine Lie Algebras and Lie Tori
- Imbedding of Jordan Algebras into Lie Algebras. I
- Lie superalgebras
- Derivations of skew polynomial rings
- The root system and the core of an extended affine Lie algebra.