CONICS FROM THE ADJOINT REPRESENTATION OF SU(2)

Authors

  • M. Crasmareanu Faculty of Mathematics, University ``Al. I.Cuza'', Iasi, 700506, România Author

Keywords:

Conic, adjoint representation of SU(2), complex variable

Subjects:

11D09, 51N20, 30C10, 22E47

Abstract

The aim of this paper is to introduce and study the class of conics provided by the symmetric matrices of the adjoint representation of the Lie group SU(2)=S3. This class depends on three real parameters as components of a point of sphere S2 and various relationships between these parameters give special subclasses of conics. A symmetric matrix inspired by one giving by Barning as Pythagorean triple preserving matrix and associated hyperbola are carefully analyzed. We extend this latter hyperbola to a class of hyperbolas with integral coefficients. A complex approach is also included.

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Published

2021-10-15