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IJPMS > IJPMS Volume 17 > Traces in SL(3,C) and SU(2,1) Groups
Traces in <i>SL</i>(3,C) and <i>SU</i>(2,1) Groups
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Traces in SL(3,C) and SU(2,1) Groups

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Abstract:

In this paper we prove some trace identities in SL(3,C) and SU(2,1) groups. We also present the merits on how to parametrise pair of pants via traces and cross-ratio. Finally, we compute traces of matrices that are generated by complex reflections in complex triangle groups.

Info:

Periodical:
International Journal of Pure Mathematical Sciences (Volume 17)
Pages:
19-29
DOI:
https://doi.org/10.18052/www.scipress.com/IJPMS.17.19
Citation:
D. Y.B. Annor and R. K. Boadi, "Traces in SL(3,C) and SU(2,1) Groups", International Journal of Pure Mathematical Sciences, Vol. 17, pp. 19-29, 2016
Online since:
October 2016
Authors:
Dickson Y.B. Annor, Richard K. Boadi
Keywords:
Cross-Ratio, Free Group, Hermitian Form, Hermitian Matrix, Special Linear Group, Special Unitary Group, Trace of a Matrix, Triangle Group
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Distribution:
Open Access

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This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

[1] S. Lawton, Generators, relations and symmetries in pairs of 3 × 3 unimodular matrices, Journal of Algebra. 313 (2007) 782-801.

[2] J.R. Parker, I.D. Platis, Complex hyperbolic Fenchel-Nielsen coordinates, Journal of Toplogy. 47 (2008) 101-135.

[3] J.R. Parker, Notes on complex hyperbolic geometry, Preprint, (2003).

[4] J. R . Parker, Traces in complex hyperbolic geometry, Geometry, Topology and Dynamics of Character Varieties. 23 (2012) 191-245.

[5] I.D. Platis, Complex cross-ratios and ptolemaean inequality, Unpublished paper, (2012).

[6] A. Pratoussevitch, Traces in complex hyperbolic triangle groups, Geometriae Dedicate. 111 (2005) 159-185.

[7] H. Sandler, Traces in SU(2, 1) and complex hyperbolic ideal triangle groups, Algebras, Groups and Geometry. 12 (1995) 139-156.

[8] P. Will, Traces, cross-ratios and 2-generator subgroups of SU(2, 1), Canad. J. Math. 61 (2009) 1407-1436.

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