On quotients of affine superschemes over finite supergroups

A. N. Zubkov

doi:10.1142/S0219498811004604

On quotients of affine superschemes over finite supergroups

A. N. Zubkov

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

14 Citations (Scopus)

Abstract

We consider an affine superscheme X over a field K, of characteristic that is different from 2, together with an action of a finite supergroup G on it. We prove that if G acts freely on X, then the sheaf quotient X/G̃ (with respect to fppf topology) is again an affine superscheme Y, where K[Y] ≃ K[X]^G. Besides, K[X] is a finitely presented progenerator as a K[X]^G-module.

Original language	English
Pages (from-to)	391-408
Number of pages	18
Journal	Journal of Algebra and its Applications
Volume	10
Issue number	3
DOIs	https://doi.org/10.1142/S0219498811004604
Publication status	Published - Jun 2011
Externally published	Yes

Keywords

Hopf superalgebra
Supergroup
affine superscheme
free action
projective progenerator
sheaf quotient

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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10.1142/S0219498811004604

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abstract = "We consider an affine superscheme X over a field K, of characteristic that is different from 2, together with an action of a finite supergroup G on it. We prove that if G acts freely on X, then the sheaf quotient X/{\~G} (with respect to fppf topology) is again an affine superscheme Y, where K[Y] ≃ K[X]G. Besides, K[X] is a finitely presented progenerator as a K[X]G-module.",

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AB - We consider an affine superscheme X over a field K, of characteristic that is different from 2, together with an action of a finite supergroup G on it. We prove that if G acts freely on X, then the sheaf quotient X/G̃ (with respect to fppf topology) is again an affine superscheme Y, where K[Y] ≃ K[X]G. Besides, K[X] is a finitely presented progenerator as a K[X]G-module.

KW - Hopf superalgebra

KW - Supergroup

KW - affine superscheme

KW - free action

KW - projective progenerator

KW - sheaf quotient

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JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

IS - 3

ER -

On quotients of affine superschemes over finite supergroups

Abstract

Keywords

ASJC Scopus subject areas

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