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
Recommended Citation
Goldberg, Vladislav V. and Shelekhov, Alexander M., "On Grassmannizable group 3-webs" (2008). Faculty Publications. 12840.
https://digitalcommons.njit.edu/fac_pubs/12840
