Orbits and invariants of the supergroup \(GQ_ n\)
type: Item
instance of: scholarly article
title: Orbits and invariants of the supergroup \(GQ_ n\)
zbMATH Open document ID: 0832.17003
DOI: 10.1007/BF01077078
author: V. N. Shander
publication date: 1993-01-16T00:00:00Z
review text: Let \(A\) be a commutative superalgebra with unit over \(\mathbb{C}\) such that \(A/ A_1\oplus (A_1)^2 \simeq \mathbb{C}\), and let \(\pi: A\to \mathbb{C}\) be the corresponding projection. Denote the algebra \(\text{Mat} (n; \mathbb{C})\) by \(Q(n; \mathbb{C})\), the group \(GL (n; \mathbb{C})\) by \(GQ(n; \mathbb{C})\), and to reduce the description of invariants and orbits of \(GQ (n; \mathbb{C})\) to the study of the action of \(S_n\) and \((A_1)^n\) on \(\mathbb{C}^n\), we consider the analogous problems for the action of the supergroup \(GQ_n\) on the supermanifold \(\widetilde {Q}_n\).
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 58A50
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 95230
zbMATH Keywords: complex supermanifold
zbMATH Keywords: commutative superalgebra
zbMATH Keywords: invariants
zbMATH Keywords: orbits
MaRDI profile type: Publication
cites work: Q3043319
full work available at URL: https://doi.org/10.1007/bf01077078
OpenAlex ID: W2052196827
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 95230