Summary
Let G be a connected complex algebraic group and A an abelian connected algebraic group, together with an algebraic action of G on A via group automorphisms. The aim of this article is to study the group of isomorphism classes of extensions of G by A in the algebraic group category. We describe this group as a direct sum of the group Hom (π 1([G, G]), A) and a relative Lie algebra cohomology space. We also prove a version of Van Est’s theorem for algebraic groups, identifying the cohomology of G with values in a G-module a in terms of relative Lie algebra cohomology.
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Dedicated to Professor Anthony Joseph on his sixtieth birthday
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© 2006 Birkhäuser Boston
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Kumar, S., Neeb, KH. (2006). Extensions of algebraic groups. In: Bernstein, J., Hinich, V., Melnikov, A. (eds) Studies in Lie Theory. Progress in Mathematics, vol 243. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4478-4_13
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DOI: https://doi.org/10.1007/0-8176-4478-4_13
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4342-3
Online ISBN: 978-0-8176-4478-9
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