Twisting procedure on torogonal structures
type: Item
instance of: scholarly article
title: Twisting procedure on torogonal structures
zbMATH Open document ID: 0804.53042
DOI: 10.1016/0393-0440(94)90016-7
author: Jean Timbeau
published in: Journal of Geometry and Physics
publication date: 1995-01-12T00:00:00Z
review text: Let \((E,Q)\) be a pseudo-Euclidean vector space and denote by \((E',Q')\) its complexification. The Clifford group \(\Gamma(Q')\) is the subgroup of the Clifford algebra \(C(Q')\) consisting of the elements \(g\) which satisfy \(\alpha(g)xg^{-1}\in E'\) for all \(x\in E'\): \[ 1\to C^*\to \Gamma(Q')@> p>> O(Q')\to 1. \] Denote by \(N: \Gamma(Q')\to C\) the spinor norm morphism. The groups \(\text{Pin}(Q)\) and \(\Delta(Q)\) are defined by \(\text{Pin}(Q)= \text{Ker}(N)\cap p^{-1}(O(Q'))\), \(\Delta(Q)= N^{- 1}(S^ 1)\cap p^{-1}(O(Q))\). The torogonal group \(\Delta(Q)\) is a central extension of \(\text{Pin}(Q)\) by \(S^ 1\). In the present paper, the author studies torogonal structures on pseudo-Riemannian manifolds (existence, classification, connections and examples).
reviewed by: Thomas Friedrich
Mathematics Subject Classification ID: 53C10
zbMATH DE Number: 590049
zbMATH Keywords: Clifford algebra
zbMATH Keywords: spinor norm morphism
zbMATH Keywords: torogonal group
zbMATH Keywords: pseudo- Riemannian manifolds
MaRDI profile type: Publication
full work available at URL: 0393-0440(94)90016-7
OpenAlex ID: W2044736067
cites work: Clifford modules
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description: scientific article; zbMATH DE number 590049