Lie algebroids arising from simple group schemes

A classical construction of Atiyah assigns to any (real or complex) Lie group G, manifold M and principal homogeneous G-space P over M, a Lie algebroid over M ([1]). The spirit behind our work is to put this work within an algebraic context, replace M by a scheme X and G by a “simple” reductive grou...

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Detalles Bibliográficos
Publicado: 2017
Materias:
Kähler differentials for Lie algebras
Lie algebroids
Reductive group scheme
Scheme on Lie algebras
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v487_n_p1_Kuttler
http://hdl.handle.net/20.500.12110/paper_00218693_v487_n_p1_Kuttler
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00218693_v487_n_p1_Kuttler
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spelling paper:paper_00218693_v487_n_p1_Kuttler2023-06-08T14:42:29Z Lie algebroids arising from simple group schemes Kähler differentials for Lie algebras Lie algebroids Reductive group scheme Scheme on Lie algebras A classical construction of Atiyah assigns to any (real or complex) Lie group G, manifold M and principal homogeneous G-space P over M, a Lie algebroid over M ([1]). The spirit behind our work is to put this work within an algebraic context, replace M by a scheme X and G by a “simple” reductive group scheme G over X (in the sense of Demazure–Grothendieck) that arise naturally with an attached torsor (which plays the role of P) in the study of Extended Affine Lie Algebras (see [9] for an overview). Lie algebroids in an algebraic sense were also considered by Beilinson and Bernstein. We will explain how the present work relates to theirs. © 2017 Elsevier Inc. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v487_n_p1_Kuttler http://hdl.handle.net/20.500.12110/paper_00218693_v487_n_p1_Kuttler
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Kähler differentials for Lie algebras
Lie algebroids
Reductive group scheme
Scheme on Lie algebras
spellingShingle Kähler differentials for Lie algebras
Lie algebroids
Reductive group scheme
Scheme on Lie algebras
Lie algebroids arising from simple group schemes
topic_facet Kähler differentials for Lie algebras
Lie algebroids
Reductive group scheme
Scheme on Lie algebras
description A classical construction of Atiyah assigns to any (real or complex) Lie group G, manifold M and principal homogeneous G-space P over M, a Lie algebroid over M ([1]). The spirit behind our work is to put this work within an algebraic context, replace M by a scheme X and G by a “simple” reductive group scheme G over X (in the sense of Demazure–Grothendieck) that arise naturally with an attached torsor (which plays the role of P) in the study of Extended Affine Lie Algebras (see [9] for an overview). Lie algebroids in an algebraic sense were also considered by Beilinson and Bernstein. We will explain how the present work relates to theirs. © 2017 Elsevier Inc.
title Lie algebroids arising from simple group schemes
title_short Lie algebroids arising from simple group schemes
title_full Lie algebroids arising from simple group schemes
title_fullStr Lie algebroids arising from simple group schemes
title_full_unstemmed Lie algebroids arising from simple group schemes
title_sort lie algebroids arising from simple group schemes
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v487_n_p1_Kuttler
http://hdl.handle.net/20.500.12110/paper_00218693_v487_n_p1_Kuttler
_version_ 1768545268468285440

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