TL;DR
This paper develops a comprehensive theory of algebraic group superschemes beyond the affine case, establishing a key equivalence with Harish-Chandra pairs and exploring significant applications in supergeometry.
Contribution
It generalizes the category equivalence between algebraic group superschemes and Harish-Chandra pairs to the non-affine case, expanding the theoretical framework.
Findings
Established a category equivalence for non-affine algebraic group superschemes and Harish-Chandra pairs.
Presented a super version of the Barsotti-Chevalley Theorem.
Constructed explicit quotient superschemes for algebraic group superschemes.
Abstract
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 of an algebraic group superscheme by a group super-subscheme .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Molecular spectroscopy and chirality