Witt algebra and the curvature of the Heisenberg group

Zoltán Muzsnay; Péter T. Nagy

Communications in Mathematics (2012)

  • Volume: 20, Issue: 1, page 33-40
  • ISSN: 1804-1388

Abstract

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The aim of this paper is to determine explicitly the algebraic structure of the curvature algebra of the 3-dimensional Heisenberg group with left invariant cubic metric. We show, that this curvature algebra is an infinite dimensional graded Lie subalgebra of the generalized Witt algebra of homogeneous vector fields generated by three elements.

How to cite

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Muzsnay, Zoltán, and Nagy, Péter T.. "Witt algebra and the curvature of the Heisenberg group." Communications in Mathematics 20.1 (2012): 33-40. <http://eudml.org/doc/247235>.

@article{Muzsnay2012,
abstract = {The aim of this paper is to determine explicitly the algebraic structure of the curvature algebra of the 3-dimensional Heisenberg group with left invariant cubic metric. We show, that this curvature algebra is an infinite dimensional graded Lie subalgebra of the generalized Witt algebra of homogeneous vector fields generated by three elements.},
author = {Muzsnay, Zoltán, Nagy, Péter T.},
journal = {Communications in Mathematics},
keywords = {Finsler geometry; holonomy; infinite dimensional Lie algebra; Witt algebra; Finsler geometry; holonomy; infinite-dimensional Lie algebra; Witt algebra},
language = {eng},
number = {1},
pages = {33-40},
publisher = {University of Ostrava},
title = {Witt algebra and the curvature of the Heisenberg group},
url = {http://eudml.org/doc/247235},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Muzsnay, Zoltán
AU - Nagy, Péter T.
TI - Witt algebra and the curvature of the Heisenberg group
JO - Communications in Mathematics
PY - 2012
PB - University of Ostrava
VL - 20
IS - 1
SP - 33
EP - 40
AB - The aim of this paper is to determine explicitly the algebraic structure of the curvature algebra of the 3-dimensional Heisenberg group with left invariant cubic metric. We show, that this curvature algebra is an infinite dimensional graded Lie subalgebra of the generalized Witt algebra of homogeneous vector fields generated by three elements.
LA - eng
KW - Finsler geometry; holonomy; infinite dimensional Lie algebra; Witt algebra; Finsler geometry; holonomy; infinite-dimensional Lie algebra; Witt algebra
UR - http://eudml.org/doc/247235
ER -

References

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  1. Dokovic, D.Z., Zhao, K., 10.1090/S0002-9947-98-01786-3, T. Am. Math. Soc., 350, 2, 1998, 643-664 (1998) MR1390977DOI10.1090/S0002-9947-98-01786-3
  2. Kawamoto, N., Generalizations of Witt algebras over a field of characteristic zero, Hiroshima Math., 16, 1986, 417-426 (1986) Zbl0607.17008MR0855169
  3. Matsumoto, M., Finsler Geometry in the 20th-Century, Handbook of Finsler Geometry, 2003, Kluwer Academic Publishers, 565--966. (2003) MR2066451
  4. Muzsnay, Z., Nagy, P.T., Finsler manifolds with non-Riemannian holonomy, Houston J. Math., 38, 2012, 77-92 (2012) Zbl1238.53012MR2917275
  5. Shen, Z., Differential Geometry of Spray and Finsler Spaces, 2001, Kluwer Academic Publishers, Dordrecht (2001) Zbl1009.53004MR1967666

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