Lie algebroids arising from simple group schemes

JOURNAL OF ALGEBRA

卷:487

Article

Kuttler, Jochen¹  Pianzola, Arturo^1,2  Quallbrunn, Federico^2,3 

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[2] Ctr Altos Estudios Ciencias Exactas, Ave Mayo 866, RA-1084 Buenos Aires, DF, Argentina

[3] Univ Buenos Aires, Dept Matemat, Buenos Aires, DF, Argentina

关键词: Lie algebroids;    Reductive group scheme;    Scheme on Lie algebras;    Kahler differentials for Lie algebras;   

DOI  :  10.1016/j.jalgebra.2017.05.005

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free