Group superschemes

We develop a general theory of algebraic group superschemes, which are not necessarily affine. Our key result is a category equivalence between those group superschemes and Harish-Chandra pairs, which generalizes the result known for affine algebraic group superschemes. Then we present the applicati...

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Bibliographic Details
Published inJournal of algebra Vol. 605; pp. 89 - 145
Main Authors Masuoka, A., Zubkov, A.N.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2022
Subjects
Abelian supervarieties
Group superschemes
Harish-Chandra pairs
Hopf superalgebras
Pseudoabelian group superschemes
Sheaf quotient
Supercoalgebras
Pseudoabelian group superschemes
Supercoalgebras
Hopf superalgebras
Abelian supervarieties
Harish-Chandra pairs
Sheaf quotient
Group superschemes
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Summary:We develop a general theory of algebraic group superschemes, which are not necessarily affine. Our key result is a category equivalence between those group superschemes and Harish-Chandra pairs, which generalizes the result known for affine algebraic group superschemes. Then we present the applications, including the Barsotti-Chevalley Theorem in the super context, and an explicit construction of the quotient superscheme G/H of an algebraic group superscheme G by a group super-subscheme H.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2022.04.027