On Grassmannizable group 3-webs

Document Type

Article

Publication Date

4-1-2008

Abstract

The authors prove that the Lie group G generating a Grassmannizable group 3-web GGW is the group of parameters of the group of similarity transformations of an (r-1)-dimensional affine space Ar-1. The transitive action of the group G on itself is an r-parameter subgroup B(r) of the group A(r 2+r) of affine transformations z I =a J I x J +b I ,I,J=1,...,r, which is the direct product of the one-dimensional group of homotheties z 1=kx 1 and r-1 one-dimensional groups of affine transformations z i = kxi + bi, i = 2, ... ,r,where all r groups have the same homothety coefficient k. Conversely, the Lie group B(r) described above generates a Grassmannizable group 3-web GGW. The Lie group G is solvable but not nilpotent. © 2008 Springer Science+Business Media B.V.

Identifier

39849100383 (Scopus)

Publication Title

Acta Applicandae Mathematicae

External Full Text Location

https://doi.org/10.1007/s10440-008-9203-9

e-ISSN

15729036

ISSN

01678019

First Page

53

Last Page

57

Issue

1-3

Volume

101

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