Weakly irreducible subgroups of Sp ( 1 , n + 1 )

Natalia I. Bezvitnaya

Archivum Mathematicum (2008)

  • Volume: 044, Issue: 5, page 341-352
  • ISSN: 0044-8753

Abstract

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Connected weakly irreducible not irreducible subgroups of Sp ( 1 , n + 1 ) SO ( 4 , 4 n + 4 ) that satisfy a certain additional condition are classified. This will be used to classify connected holonomy groups of pseudo-hyper-Kählerian manifolds of index 4.

How to cite

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Bezvitnaya, Natalia I.. "Weakly irreducible subgroups of $\mbox{Sp}(1,n+1)$." Archivum Mathematicum 044.5 (2008): 341-352. <http://eudml.org/doc/261051>.

@article{Bezvitnaya2008,
abstract = {Connected weakly irreducible not irreducible subgroups of $\mbox\{Sp\}(1,n+1)\subset \mbox\{SO\}(4,4n+4)$ that satisfy a certain additional condition are classified. This will be used to classify connected holonomy groups of pseudo-hyper-Kählerian manifolds of index 4.},
author = {Bezvitnaya, Natalia I.},
journal = {Archivum Mathematicum},
keywords = {pseudo-hyper-Kählerian manifold of index 4; weakly irreducible holonomy group; pseudo-hyper-Kählerian manifold of index 4; weakly irreducible holonomy group},
language = {eng},
number = {5},
pages = {341-352},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Weakly irreducible subgroups of $\mbox\{Sp\}(1,n+1)$},
url = {http://eudml.org/doc/261051},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Bezvitnaya, Natalia I.
TI - Weakly irreducible subgroups of $\mbox{Sp}(1,n+1)$
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 5
SP - 341
EP - 352
AB - Connected weakly irreducible not irreducible subgroups of $\mbox{Sp}(1,n+1)\subset \mbox{SO}(4,4n+4)$ that satisfy a certain additional condition are classified. This will be used to classify connected holonomy groups of pseudo-hyper-Kählerian manifolds of index 4.
LA - eng
KW - pseudo-hyper-Kählerian manifold of index 4; weakly irreducible holonomy group; pseudo-hyper-Kählerian manifold of index 4; weakly irreducible holonomy group
UR - http://eudml.org/doc/261051
ER -

References

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  8. Galaev, A. S., Isometry groups of Lobachevskian spaces, similarity transformation groups of Euclidian spaces and Lorentzian holonomy groups, Rend. Circ. Mat. Palermo (2) Suppl. 79 (2006), 87–97. (2006) MR2287128
  9. Galaev, A. S., 10.1142/S0219887806001570, Internat. J. Geom. Meth. Modern Phys. 3 (5, 6) (2006), 1025–1045. (2006) Zbl1112.53039MR2264404DOI10.1142/S0219887806001570
  10. Joyce, D., Compact manifolds with special holonomy, Oxford University Press, 2000. (2000) Zbl1027.53052MR1787733
  11. Leistner, T., On the classification of Lorentzian holonomy groups, J. Differential Geom. 76 (3) (2007), 423–484. (2007) Zbl1129.53029MR2331527
  12. Wu, H., 10.2140/pjm.1967.20.351, Pacific J. Math. 20 (1967), 351–382. (1967) Zbl0149.39603MR0212740DOI10.2140/pjm.1967.20.351

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