Differentials for Lie algebras

We develop a theory of relative Kähler differentials for Lie algebras. The main result is that the functor of relative differentials is representable, and that the universal object which represents it behaves properly with respect to étale base change. We illustrate how our construction yields a det...

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Bibliographic Details
Published inAlgebras and representation theory Vol. 18; no. 4; pp. 941 - 960
Main Authors Kuttler, Jochen, Pianzola, Arturo
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.08.2015
Subjects
Associative Rings and Algebras
Commutative Rings and Algebras
Mathematics
Mathematics and Statistics
Non-associative Rings and Algebras
Relative Kähler differentials of Lie algebras
Centroid
12G05
Twisted form
Primary 17B67; Secondary 17B01
Faithfully flat descent
20G10
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Summary:We develop a theory of relative Kähler differentials for Lie algebras. The main result is that the functor of relative differentials is representable, and that the universal object which represents it behaves properly with respect to étale base change. We illustrate how our construction yields a detailed analysis of the structure of derivations of multiloop algebras which is needed for the construction of Extended Affine Lie Algebras.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-015-9526-y