Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T16:42:29.714Z Has data issue: false hasContentIssue false
  • English
  • Français

On the classification of the real vector subspaces of a quaternionic vector space

Part of: Basic constructions Categories and geometry Global differential geometry

Published online by Cambridge University Press:  03 April 2013

Radu Pantilie
Radu Pantilie*
Affiliation:
Institutul de Matematică ‘Simion Stoilow’ al Academiei Române, CP 1-764, 014700 Bucureşti, Romania (radu.pantilie@imar.ro)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove the classification of the real vector subspaces of a quaternionic vector space by using a covariant functor which associates, to any pair formed of a quaternionic vector space and a real subspace, a coherent sheaf over the sphere.

Keywords

quaternionic geometrysheaves over the sphere

MSC classification

Secondary: 18F20: Presheaves and sheaves 53C26: Hyper-Kähler and quaternionic Kähler geometry, “special” geometry 53C28: Twistor methods 54B40: Presheaves and sheaves
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 2 , June 2013 , pp. 615 - 622
Copyright
Copyright © Edinburgh Mathematical Society 2013

References

1.Alekseevsky, D. V. and Marchiafava, S., Quaternionic structures on a manifold and subordinated structures, Annali Mat. Pura Appl. 171 (1996), 205–273.CrossRefGoogle Scholar
2.Dlab, V. and Ringel, C. M., Real subspaces of a quaternion vector space, Can. J. Math. 30 (1978), 1228–1242.CrossRefGoogle Scholar
3.Gunning, R. C. and Rossi, H., Analytic functions of several complex variables (Prentice-Hall, Englewood Cliffs, NJ, 1965).Google Scholar
4.Ianuş, S., Marchiafava, S., Ornea, L. and Pantilie, R., Twistorial maps between quaternionic manifolds, Annali Scuola Norm. Sup. Pisa V 9 (2010), 47–67.Google Scholar
5.Joyce, D., Hypercomplex algebraic geometry, Q. J. Math. 49 (1998), 129–162.Google Scholar
6.Marchiafava, S., Ornea, L. and Pantilie, R., Twistor theory for CR quaternionic manifolds and related structures, Monatsh. Math. 167 (2012), 531–545.CrossRefGoogle Scholar
7.Quillen, D., Quaternionic algebra and sheaves on the Riemann sphere, Q. J. Math. 49 (1998), 163–198.CrossRefGoogle Scholar
8.Widdows, D., Quaternionic algebra described by Sp(1) representations, Q. J. Math. 54 (2003), 463–481.CrossRefGoogle Scholar