Gerbal central extensions of reductive groups by K3

Pavel Safronov

doi:10.1016/j.jalgebra.2015.07.034

Gerbal central extensions of reductive groups by K3

Pavel Safronov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We classify central extensions of a reductive group G by K3 and BK3, the sheaf of third Quillen K-theory groups and its classifying stack. These turn out to be parametrized by the group of Weyl-invariant quadratic forms on the cocharacter lattice valued in k× and the group of integral Weyl-invariant cubic forms on the cocharacter lattice respectively.

Original language	English
Pages (from-to)	152-182
Journal	Journal of Algebra
Volume	444
Early online date	26 Aug 2015
DOIs	https://doi.org/10.1016/j.jalgebra.2015.07.034
Publication status	Published - 15 Dec 2015

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10.1016/j.jalgebra.2015.07.034

1407.4113Accepted author manuscript, 254 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND)

https://arxiv.org/abs/1407.4113

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abstract = "We classify central extensions of a reductive group G by K3 and BK3, the sheaf of third Quillen K-theory groups and its classifying stack. These turn out to be parametrized by the group of Weyl-invariant quadratic forms on the cocharacter lattice valued in k× and the group of integral Weyl-invariant cubic forms on the cocharacter lattice respectively. ",

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AB - We classify central extensions of a reductive group G by K3 and BK3, the sheaf of third Quillen K-theory groups and its classifying stack. These turn out to be parametrized by the group of Weyl-invariant quadratic forms on the cocharacter lattice valued in k× and the group of integral Weyl-invariant cubic forms on the cocharacter lattice respectively.

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JO - Journal of Algebra

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Gerbal central extensions of reductive groups by K3

Abstract

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