Quaternionic complexes
type: Item
instance of: scholarly article
title: Quaternionic complexes
zbMATH Open document ID: 0764.53022
DOI: 10.1016/0393-0440(92)90042-Y
author: Robert J. Baston
published in: Journal of Geometry and Physics
publication date: 1992-06-28T00:00:00Z
review text: The author studies a quaternion analogue of Dolbeault cohomology obtained by extending the Moisil-Fueter operator from quaternion analysis to a locally exact complex. He uses some Bernstein-Gelfand-Gelfand complexes in representation theory, the Penrose transform and the twistor theory of quaternionic manifolds. The obtained complexes correspond to the semiregular orbits of the Weyl group of \(\text{sl}(2n+2,\mathbb{C})\). In the hyper-Kähler case the author computes the index of these complexes showing that the obtained quaternion cohomology is not trivial.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 55N30
Mathematics Subject Classification ID: 32C35
zbMATH DE Number: 34537
zbMATH Keywords: Dolbeault cohomology
zbMATH Keywords: Moisil-Fueter operator
zbMATH Keywords: Bernstein-Gelfand-Gelfand complexes
zbMATH Keywords: quaternion cohomology
reviewed by: Vasile Oproiu
MaRDI profile type: Publication
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full work available at URL: 0393-0440(92)90042-y
OpenAlex ID: W4212867687
description: scientific article; zbMATH DE number 34537