Realization of graded-simple algebras as loop algebras

DOI10.1515/FORUM.2008.020zbMath1157.17009arXivmath/0511723OpenAlexW2043960039MaRDI QIDQ3516716

Bruce N. Allison, Stephen Berman, Arturo Pianzola, John R. Faulkner

Publication date: 11 August 2008

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0511723

zbMATH Keywords

graded algebras

Mathematics Subject Classification ID

Graded Lie (super)algebras (17B70) Graded rings and modules (associative rings and algebras) (16W50)

Related Items (36)

Derivations of certain algebras defined by étale descent ⋮ Gradings on classical central simple real Lie algebras ⋮ Gradings on the Albert algebra and on \(\mathfrak{f}_4\) ⋮ Representations of toroidal extended affine Lie algebras ⋮ Integrable modules for Lie tori ⋮ Graded simple modules and loop modules ⋮ Toroidal vertex algebras and their modules ⋮ Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2 ⋮ Modules of highest weight type for the algebra of derivations over a rational quantum torus ⋮ Extended affine Lie superalgebras and their affinizations ⋮ Graded-simple algebras and cocycle twisted loop algebras ⋮ Irreducible finite-dimensional representations of equivariant map algebras ⋮ Graded modules over simple Lie algebras ⋮ Remarks on the Isotriviality of Multiloop Algebras ⋮ Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras – A Survey ⋮ Lie Groups of Bundle Automorphisms and Their Extensions ⋮ Galois cohomology and forms of algebras over Laurent polynomial rings ⋮ Thin coverings of modules ⋮ Isotriviality and étale cohomology of Laurent polynomial rings ⋮ Classification of involutions on graded-division simple real algebras ⋮ Graded simple Lie algebras and graded simple representations ⋮ On the cohomology of vector fields on parallelizable manifolds ⋮ Multiloop Lie algebras and the construction of extended affine Lie algebras ⋮ Graded division algebras over the field of real numbers ⋮ Descent constructions for central extensions of infinite dimensional Lie algebras ⋮ Gradings on semisimple algebras ⋮ Universal central extensions of twisted forms of split simple Lie algebras over rings ⋮ Graded-division algebras and Galois extensions ⋮ Torsors, reductive group schemes and extended affine Lie algebras ⋮ Multiloop realization of extended affine Lie algebras and Lie tori ⋮ Graded-division algebras over arbitrary fields ⋮ Representations of Graded Multiloop Lie Algebras ⋮ On nonassociative graded-simple algebras over the field of real numbers ⋮ Integral structures in extended affine Lie algebras ⋮ IRREDUCIBLE HARISH CHANDRA MODULES OVER THE DERIVATION ALGEBRAS OF RATIONAL QUANTUM TORI ⋮ Gradings on tensor products of composition algebras and on the Smirnov algebra

Cites Work

• The centroid of extended affine and root graded Lie algebras
• Coordinate algebras of extended affine Lie algebras of type \(A_1\)
• The Alternative Torus and the Structure of Elliptic Quasi-Simple Lie Algebras of Type A 2
• Group gradings on associative algebras

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