Vanishing of \(H^1\) for Dedekind rings and applications to loop algebras

DOI10.1016/j.crma.2005.03.022zbMath1078.14064OpenAlexW2066318054MaRDI QIDQ556912

Arturo Pianzola

Publication date: 23 June 2005

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2005.03.022

zbMATH Keywords

Kac-moody Lie algebras

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Geometric invariant theory (14L24) Lie algebras of linear algebraic groups (17B45)

Related Items (18)

Twisted forms of differential Lie algebras over \(\mathbb{C}(t)\) associated with complex simple Lie algebras ⋮ The Automorphism Group Functor of the N = 4 Lie Conformal Superalgebra ⋮ Differential conformal superalgebras and their forms ⋮ Derivations of certain algebras defined by étale descent ⋮ Classification of \(D\)-bialgebra structures on power series algebras ⋮ Descent study of the Lie algebra of derivations of certain infinite-dimensional Lie algebras ⋮ Affine Kac-Moody groups and Lie algebras in the language of SGA3 ⋮ Étale descent of derivations ⋮ Automorphisms of toroidal Lie superalgebras ⋮ Remarks on the Isotriviality of Multiloop Algebras ⋮ Galois cohomology and forms of algebras over Laurent polynomial rings ⋮ Differentials for Lie algebras ⋮ Isotriviality and étale cohomology of Laurent polynomial rings ⋮ Conjugacy theorems for loop reductive group schemes and Lie algebras ⋮ Descent constructions for central extensions of infinite dimensional Lie algebras ⋮ Universal central extensions of twisted forms of split simple Lie algebras over rings ⋮ Torsors, reductive group schemes and extended affine Lie algebras ⋮ Invariant bilinear forms of algebras given by faithfully flat descent

Cites Work

• Principal homogeneous spaces under flasque tori; applications
• Affine Kac-Moody Lie algebras as torsors over the punctured line
• Homogeneous spaces and arithmetic of reductive group schemes over Dedekind rings
• Schémas en groupes. I: Propriétés générales des schémas en groupes. Exposés I à VIIb. Séminaire de Géométrie Algébrique 1962/64, dirigé par Michel Demazure et Alexander Grothendieck. Revised reprint
• Covering algebras II: Isomorphism of loop algebras
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