A theory of extended lie transformation groups

1963 ◽  
Vol 61 (1) ◽  
pp. 247-333
Author(s):  
Tsurusaburo Takasu
Keyword(s):  
Transformation Groups ◽  
Lie Transformation

Visual Illusions of Angle as an Application of Lie Transformation Groups

SIAM Review ◽  
1971 ◽  
Vol 13 (2) ◽  
pp. 169-184 ◽  
Author(s):  
William C. Hoffman
Keyword(s):  
Visual Illusions ◽  
Transformation Groups ◽  
Lie Transformation

Lie Transformation Groups and Geometry

2012 ◽  
Author(s):  
Andreas Arvanitoyeorgos
Keyword(s):  
Transformation Groups ◽  
Lie Transformation

Pattern Recognition in Kittens: Performance on Lie Patterns

Perception ◽  
1983 ◽  
Vol 12 (4) ◽  
pp. 393-410 ◽  
Author(s):  
Peter C Dodwell ◽  
Frances E Wilkinson ◽  
Michael W von Grünau
Keyword(s):  
Experimental Study ◽  
Pattern Recognition ◽  
Pattern Analysis ◽  
Transformation Group ◽  
Transformation Groups ◽  
Continuous Transformation ◽  
Anatomy And Physiology ◽  
Visual Behaviour ◽  
Lie Transformation ◽  
Pattern Information

Despite a vast accumulation of knowledge about the anatomy and physiology of the cat's visual system in recent years, and about its early development, there has been very little experimental study of the development of visual behaviour in this species. This is especially true of the kitten's ability to recognize patterns. Two experiments are reported that aim to remedy some part of this deficiency, and that also serves to examine a particular hypothesis about the basis of pattern analysis in the young organism. This is Hoffman's hypothesis that the orbits of elementary Lie transformation groups (a species of continuous transformation group) represent the basis for coding pattern information.

scholarly journals Multilocal invariants for the classical groups

2003 ◽  
Vol 2003 (1) ◽  
pp. 27-63
Author(s):  
Paul F. Dhooghe
Keyword(s):  
Lie Algebra ◽  
Higher Order ◽  
Transformation Groups ◽  
Representation Space ◽  
Classical Groups ◽  
Invariant Polynomials ◽  
Lie Transformation ◽  
Capelli Identities

Multilocal higher-order invariants, which are higher-order invariants defined at distinct points of representation space, for the classical groups are derived in a systematic way. The basic invariants for the classical groups are the well-known polynomial or rational invariants as derived from the Capelli identities. Higher-order invariants are then constructed from the former ones by means of total derivatives. At each order, it appears that the invariants obtained in this way do not generate all invariants. The necessary additional invariants are constructed from the invariant polynomials on the Lie algebra of the Lie transformation groups.

Sign in / Sign up

Export Citation Format

Share Document