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Some complements to the Lazard isomorphism

Part of: Homology and homotopy of topological groups and related structures Lie groups Lie algebras and Lie superalgebras Linear algebraic groups and related topics

Published online by Cambridge University Press:  22 June 2010

Annette Huber ,
Guido Kings  and
Niko Naumann
Annette Huber
Affiliation:
Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, 79104 Freiburg, Germany (email: annette.huber@math.uni-freiburg.de)
Guido Kings
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany (email: guido.kings@mathematik.uni-regensburg.de)
Niko Naumann
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany (email: niko.naumann@mathematik.uni-regensburg.de)
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Abstract

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Lazard showed in his seminal work (Groupes analytiques p-adiques, Publ. Math. Inst. Hautes Études Sci. 26 (1965), 389–603) that for rational coefficients, continuous group cohomology of p-adic Lie groups is isomorphic to Lie algebra cohomology. We refine this result in two directions: first, we extend Lazard’s isomorphism to integral coefficients under certain conditions; and second, we show that for algebraic groups over finite extensions K/ℚp, his isomorphism can be generalized to K-analytic cochains andK-Lie algebra cohomology.

Keywords

Lazard isomorphismcontinuous cohomologycohomology of Lie groups and algebras

MSC classification

Secondary: 17B56: Cohomology of Lie (super)algebras 20G25: Linear algebraic groups over local fields and their integers 22E41: Continuous cohomology 57T10: Homology and cohomology of Lie groups
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 1 , January 2011 , pp. 235 - 262
Copyright
Copyright © Foundation Compositio Mathematica 2010

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