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Gerbal central extensions of reductive groups by $K_3$

Abstract:
We classify central extensions of a reductive group $G$ by $\mathcal{K}_3$ and $B\mathcal{K}_3$, 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 $k^\times$ and the group of integral Weyl-invariant cubic forms on the cocharacter lattice respectively.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Publisher:
Elsevier Publisher's website
Journal:
Journal of Algebra Journal website
Volume:
444
Pages:
152-182
Publication date:
2015-12-05
DOI:
EISSN:
1090-266X
ISSN:
0021-8693
URN:
uuid:a4f91db1-0909-443a-a93c-f4660108b335
Source identifiers:
511459
Local pid:
pubs:511459

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