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arXiv · 1707.01349

The groups of two by two matrices in double and dual numbers, and associated M\"obius transformations

Khawlah A. Mustafa
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Abstract

M\"obius transformations have been studied over the field of complex numbers. In this paper, we investigate M\"obius transformations over two rings which are not fields: the ring of double numbers and the ring of dual numbers. We give types of continuous one-parameter subgroups of $\GL{\fpower{\BR}},$ $\SL{\fpower{\BR}},$ $\GL{\BD},$ and $\SL{\BD}.$

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Khawlah A. Mustafa. 2017-07-03. The groups of two by two matrices in double and dual numbers, and associated M\"obius transformations. https://arxiv.org/abs/1707.01349

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