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Article

Muzsnay, Zoltán ; Nagy, Péter T.
Witt algebra and the curvature of the Heisenberg group. (English). Communications in Mathematics, vol. 20 (2012), issue 1, pp. 33-40
MSC: 17B65, 22E65, 53B40, 53C60 | MR 3001630 | Zbl 06202717
Keywords:
Finsler geometry; holonomy; infinite dimensional Lie algebra; Witt algebra
Summary:
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.
References:
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[4] Muzsnay, Z., Nagy, P.T.: Finsler manifolds with non-Riemannian holonomy. Houston J. Math., 38, 2012, 77-92 MR 2917275 | Zbl 1238.53012
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