Central Automorphisms Of Laguerre Planes

1998 ◽  
Vol 31 (4) ◽  
Author(s):  
H. Makowiecka ◽  
A. Matraś
Keyword(s):  
Laguerre Planes ◽  
Central Automorphisms

scholarly journals A FLAT LAGUERRE PLANE OF KLEINEWILLINGHÖFER TYPE V

2011 ◽  
Vol 91 (2) ◽  
pp. 257-274 ◽  
Author(s):  
JEROEN SCHILLEWAERT ◽  
GÜNTER F. STEINKE
Keyword(s):  
Parameter Family ◽  
Laguerre Plane ◽  
The Other ◽  
Flat Laguerre Plane ◽  
Laguerre Planes ◽  
Type V ◽  
Central Automorphisms ◽  
Kleinewillinghöfer Type

AbstractThe Kleinewillinghöfer types of Laguerre planes reflect the transitivity properties of certain groups of central automorphisms. Polster and Steinke have shown that some of the conceivable types for flat Laguerre planes cannot exist and given models for most of the other types. The existence of only a few types is still in doubt. One of these is type V.A.1, whose existence we prove here. In order to construct our model, we make systematic use of the restrictions imposed by the group. We conjecture that our example belongs to a one-parameter family of planes all of type V.A.1.

A FAMILY OF TWO-DIMENSIONAL LAGUERRE PLANES OF KLEINEWILLINGHÖFER TYPE II.A.2

2018 ◽  
Vol 105 (3) ◽  
pp. 366-379
Author(s):  
GÜNTER F. STEINKE
Keyword(s):  
Two Dimensional ◽  
Transitive Groups ◽  
Laguerre Planes ◽  
Translation Type ◽  
Central Automorphisms ◽  
Existence Question ◽  
Kleinewillinghöfer Type

Kleinewillinghöfer classified Laguerre planes with respect to linearly transitive groups of central automorphisms. Polster and Steinke investigated two-dimensional Laguerre planes and their so-called Kleinewillinghöfer types. For some of the feasible types the existence question remained open. We provide examples of such planes of type II.A.2, which are based on certain two-dimensional Laguerre planes of translation type. With these models only one type, I.A.2, is left for which no two-dimensional Laguerre planes are known yet.

scholarly journals A family of 2-dimensional Laguerre planes of generalised shear type

2000 ◽  
Vol 61 (1) ◽  
pp. 69-83 ◽  
Author(s):  
B. Polster ◽  
G. F. Steinke
Keyword(s):  
Shear Type ◽  
Laguerre Planes ◽  
Central Automorphisms

We construct a family of 2-dimensional Laguerre planes that generalises ovoidal Laguerre planes and the Laguerre planes of shear type, as described by Löwen and Pfüller, by gluing together circle sets from up to eight different ovoidal Laguerre planes. Each plane in this family admits all maps (x, y) ↦ (x, ry) for r > 0 as central automorphisms at the circle y = 0.

On the Kleinewillinghöfer types of flat Laguerre planes

2004 ◽  
Vol 46 (1-2) ◽  
pp. 103-122 ◽  
Author(s):  
Burkard Polster ◽  
Günter F. Steinke
Keyword(s):  
Laguerre Planes

AUTOMORPHISMS OF BRAID GROUPS ON S2, T2, P2 AND THE KLEIN BOTTLE K

2008 ◽  
Vol 17 (01) ◽  
pp. 47-53 ◽  
Author(s):  
PING ZHANG
Keyword(s):  
Braid Group ◽  
Mapping Class Group ◽  
Class Group ◽  
Klein Bottle ◽  
Closed Surface ◽  
Group Extension ◽  
Braid Groups ◽  
Mapping Class ◽  
Group B ◽  
Central Automorphisms

It is shown that for the braid group Bn(M) on a closed surface M of nonnegative Euler characteristic, Out (Bn(M)) is isomorphic to a group extension of the group of central automorphisms of Bn(M) by the extended mapping class group of M, with an explicit and complete description of Aut (Bn(S2)), Aut (Bn(P2)), Out (Bn(S2)) and Out (Bn(P2)).

Central automorphisms of free nilpotent Lie algebras

2017 ◽  
Vol 16 (11) ◽  
pp. 1750205
Author(s):  
Özge Öztekin ◽  
Naime Ekici
Keyword(s):  
Lie Algebras ◽  
Finite Rank ◽  
Characteristic Zero ◽  
Sufficient Conditions ◽  
Nilpotency Class ◽  
Nilpotent Lie Algebra ◽  
Central Automorphism ◽  
Nilpotent Lie Algebras ◽  
Central Automorphisms

Let [Formula: see text] be the free nilpotent Lie algebra of finite rank [Formula: see text] [Formula: see text] and nilpotency class [Formula: see text] over a field of characteristic zero. We give a characterization of central automorphisms of [Formula: see text] and we find sufficient conditions for an automorphism of [Formula: see text] to be a central automorphism.

Sign in / Sign up

Export Citation Format

Share Document