New Representation of Quaternions Lie Group and SU(2)

Year 2013, Volume: 10 Issue: 1, - , 01.05.2013

Ali Delbaznasab Mohammad Reza Molaei

Abstract

In this paper the concept of outer product for R
4
is considered. By using this
outer product a new product on R
5
is introduced. R
5 with this product and usual addition
and scalar multiplication is an associative algebra. Via this algebra a new representation
for quaternions as a Lie group is presented. Moreover a representation for SU(2) is
deduced. 

Keywords

Orthogonal Lie group, outer product, representation

References

• [1] R. Abraham, J. E. Marsden and T. Ratiu, Manifolds, Tensor Analysis, and Applications, Addison-Wesley, 1983.
• [2] A. Baker, Matrix Groups an Introduction to Lie Group Theory, Springer-Verlag, 2002.
• [3] W. Fulton and J. Harris, Representation Theory. A First Course, Springer-Verlag, 1991.
• [4] P. R. Girard, Quaternion, Clifford Algebras and Relativistic Physics, Birkhauser, 2007.
• [5] B. C. Hall, Lie Groups Lie Algebras, and Representation, Springer-Verlag, 2004.
• [6] J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry, Springer-Verlag, 1999.
• [7] D. Miliˇci´c, Lectures on Lie Groups, http://www.math.utah.edu/~milicic/Eprints/ lie.pdf, 2004.
• [8] M. R. Molaei and M.R. Farhangdost, Lie algebras of a class of top spaces, Balkan Journal of Geometry and Its Applications 14 (2009), 46–51.
• [9] O. Raifeartaigh, Group Structure of Gauge Theories, Cambridge University Press, 1986.
• [10] R. Penrose and W. Rindler, Spinors and Space-Time, Cambridge University Press, 1984.