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Schreier loops

Péter T. NagyKarl Strambach — 2008

Czechoslovak Mathematical Journal

We study systematically the natural generalization of Schreier's extension theory to obtain proper loops and show that this construction gives a rich family of examples of loops in all traditional common, important loop classes.

Tangent Lie algebras to the holonomy group of a Finsler manifold

Zoltán MuzsnayPéter T. Nagy — 2011

Communications in Mathematics

Our goal in this paper is to make an attempt to find the largest Lie algebra of vector fields on the indicatrix such that all its elements are tangent to the holonomy group of a Finsler manifold. First, we introduce the notion of the curvature algebra, generated by curvature vector fields, then we define the infinitesimal holonomy algebra by the smallest Lie algebra of vector fields on an indicatrix, containing the curvature vector fields and their horizontal covariant derivatives with respect to...

Quasigroups arisen by right nuclear extension

Péter T. NagyIzabella Stuhl — 2012

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to prove that a quasigroup Q with right unit is isomorphic to an f -extension of a right nuclear normal subgroup G by the factor quasigroup Q / G if and only if there exists a normalized left transversal Σ Q to G in Q such that the right translations by elements of Σ commute with all right translations by elements of the subgroup G . Moreover, a loop Q is isomorphic to an f -extension of a right nuclear normal subgroup G by a loop if and only if G is middle-nuclear, and there exists...

Witt algebra and the curvature of the Heisenberg group

Zoltán MuzsnayPéter T. Nagy — 2012

Communications in Mathematics

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.

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