The General Projective Group

Sophus Lie

Chapter Chapter 26 in Theory of Transformation Groups I, 2015, pp 559-580 from Springer

Abstract: Abstract The equations: $$ x_\nu ' = \frac{a_{1\nu }\,x_1+\cdots +a_{n\nu }\,x_n+a_{n+1,\nu }}{ a_{1,n+1}\,x_1+\cdots +a_{n,n+1}\,x_n+a_{n+1,n+1}}\qquad {\scriptstyle {(\nu \,=\,1\,\cdots \,n)}}\quad {(1)} $$ x ν ′ = a 1 ν x 1 + ⋯ + a n ν x n + a n + 1 , ν a 1 , n + 1 x 1 + ⋯ + a n , n + 1 x n + a n + 1 , n + 1 ( ν = 1 ⋯ n ) ( 1 ) determine a group, as one easily convinces oneself, the so-called general projective group of the manifold $$x_1, \dots , x_n$$ x 1 , ⋯ , x n . In the present chapter, we want to study more closely this important group, which is also called the group of all collineations [Collineationen] of the space $$x_1, \dots , x_n$$ x 1 , ⋯ , x n , by focusing our attention on its subgroups.

Keywords: Linear Transformation; Linear Group; Invariant Manifold; Projective Group; Projective Transformation (search for similar items in EconPapers)
Date: 2015
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-46211-9_26

Ordering information: This item can be ordered from
http://www.springer.com/9783662462119

DOI: 10.1007/978-3-662-46211-9_26

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().