# Witt algebra and the curvature of the Heisenberg group

Communications in Mathematics (2012)

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

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topMuzsnay, 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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- Kawamoto, N., Generalizations of Witt algebras over a field of characteristic zero, Hiroshima Math., 16, 1986, 417-426 (1986) Zbl0607.17008MR0855169
- Matsumoto, M., Finsler Geometry in the 20th-Century, Handbook of Finsler Geometry, 2003, Kluwer Academic Publishers, 565--966. (2003) MR2066451
- Muzsnay, Z., Nagy, P.T., Finsler manifolds with non-Riemannian holonomy, Houston J. Math., 38, 2012, 77-92 (2012) Zbl1238.53012MR2917275
- Shen, Z., Differential Geometry of Spray and Finsler Spaces, 2001, Kluwer Academic Publishers, Dordrecht (2001) Zbl1009.53004MR1967666

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