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Submaximally symmetric almost quaternionic structures

Permanent link
https://hdl.handle.net/10037/13051
DOI
https://doi.org/10.1007/s00031-017-9453-6
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Date
2017-11-10
Type
Journal article
Tidsskriftartikkel
Peer reviewed

Author
Kruglikov, Boris; Winther, Henrik; Zalabová, Lenka
Abstract
The symmetry dimension of a geometric structure is the dimension of its symmetry algebra. We investigate symmetries of almost quaternionic structures of quaternionic dimension n. The maximal possible symmetry is realized by the quaternionic projective space HP n, which is flat and has the symmetry algebra sl(n + 1, H) of dimension 4n 2 + 8n + 3. For non-flat almost quaternionic manifolds we compute the next biggest (submaximal) symmetry dimension. We show that it is equal to 4n 2−4n+9 for n > 1 (it is equal to 8 for n = 1). This is realized both by a quaternionic structure (torsion–free) and by an almost quaternionic structure with vanishing quaternionic Weyl curvature.
Description
This is a post-peer-review, pre-copyedit version of an article published in Transformation groups. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00031-017-9453-6.
Publisher
Springer Verlag
Citation
Kruglikov, B., Winther, H. & Zalabová, L. (2017). Submaximally symmetric almost quaternionic structures. Transformation groups, 1-19.
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