Adjoint representations for SU(2), su(2) and sl(2)

Saad Owaid; Zainab Subhi

doi:10.23851/mjs.v27i5.171

Authors

Saad Owaid Department of Mathematics, Faculty of Science, Al-Mustansiriyah University, Baghdad
Zainab Subhi Department of Mathematics, Faculty of Science, Al-Mustansiriyah University, Baghdad

DOI:

https://doi.org/10.23851/mjs.v27i5.171

Keywords:

unitary matrix, SU(2), Lie group, representation theory

Abstract

This work, presents four kinds of adjoint representations for the special unitary matrix Lie group SU(2) and the special unitary, special linear matrix Lie algebras su(2) and sl(2). In the first two we assume the vector spaces as the matrix Lie algebras su(2) and sl(2), later cases obtained by exploiting the action of su(2) and sl(2) on themselves. Also, we compute their direct sums. The results have been displayed as Tables in a nice form.

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References

Baker A., " An introduction to matrix groups and their applications ", Scotland, University of Glasgow, 2000.

Bourbaki, N., "General Topology", 2ndedSpringer-Verlag, New York, London, 1989.

https://doi.org/10.1007/978-3-642-61703-4

Curtis, M., "Matrix Groups", 2nd ed. Springer-Verlag, New York, 1984.

https://doi.org/10.1007/978-1-4612-5286-3

Fulton, W., and Harris, J.," Representation Theory", Springer-Verlag, New York, INC, 1991.

Hall, B. C., "Lie Groups, Lie Algebras and Representations, An Elementary Introduction", Springer, USA, May, 2004.

Helmer A.,"Determining summands in tensor products of Lie algebra representations", National University of Singapore, Singapore 0511, Singapore, 15 June 1992.

Mahmoud A. A. Sbaih, Moeen KH. Srour, M. S. Hamada and H. M. Fayad, "Lie Algebra and Representation of SU(4)", Al Aqsa University, P. O. Box 4501, Gaza, Palestine, EJTP 10, No. 28 (2013) 9–26.

Sattinger, D. H., "Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics", Springer-Verlag, New York, Applied Mathematical Sciences, Volume 61, (1985), pp.164-180.