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Algebraic supergroups and Harish-Chandra pairs over a commutative ring


Authors: Akira Masuoka and Taiki Shibata
Journal: Trans. Amer. Math. Soc. 369 (2017), 3443-3481
MSC (2010): Primary 14M30, 16T05, 16W55
DOI: https://doi.org/10.1090/tran/6751
Published electronically: September 27, 2016
MathSciNet review: 3605977
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Abstract: We prove a category equivalence between algebraic supergroups and Harish-Chandra pairs over a commutative ring which is $ 2$-torsion free. The result is applied to reconstruct the Chevalley $ \mathbb{Z}$-supergroups constructed by Fioresi and Gavarini (2012) and by Gavarini (2014). For a wide class of algebraic supergroups we describe their representations by using their super-hyperalgebras.


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Additional Information

Akira Masuoka
Affiliation: Institute of Mathematics, University of Tsukuba, Ibaraki 305-8571, Japan
Email: akira@math.tsukuba.ac.jp

Taiki Shibata
Affiliation: Graduate School of Pure and Applied Sciences, University of Tsukuba, Ibaraki 305-8571, Japan
Address at time of publication: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Email: shibata@ualberta.ca

DOI: https://doi.org/10.1090/tran/6751
Keywords: Algebraic supergroup, Hopf superalgebra, Harish-Chandra pair, super-hyperalgebra, Chevalley supergroup
Received by editor(s): May 30, 2013
Received by editor(s) in revised form: March 22, 2015, and May 9, 2015
Published electronically: September 27, 2016
Additional Notes: The first author was supported by JSPS Grant-in-Aid for Scientific Research (C) 23540039
The second author was supported by Grant-in-Aid for JSPS Fellows 26E2022
Article copyright: © Copyright 2016 American Mathematical Society

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