Extension of Local Loop Isomorphisms.
Invariant tensorfields and the canonical connection of a 3-web.
Tangent Lie algebras to the holonomy group of a Finsler manifold
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
The aim of this paper is to prove that a quasigroup with right unit is isomorphic to an -extension of a right nuclear normal subgroup by the factor quasigroup if and only if there exists a normalized left transversal to in such that the right translations by elements of commute with all right translations by elements of the subgroup . Moreover, a loop is isomorphic to an -extension of a right nuclear normal subgroup by a loop if and only if is middle-nuclear, and there exists...
Witt algebra and the curvature of the Heisenberg group
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.
Schreier loops
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.
Inverse property of nonassociative abelian extensions
Our paper deals with the investigation of extensions of commutative groups by loops so that the quasigroups that result in the multiplication between cosets of the kernel subgroup are T-quasigroups. We limit our study to extensions in which the quasigroups determining the multiplication are linear functions without constant term, called linear abelian extensions. We characterize constructively such extensions with left-, right-, or inverse properties using a general construction according to an...
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