Dense 2-generator subsemigroups of $2\times 2$ matrices

Details Dense 2-generator subsemigroups of $2\times 2$ matrices Dense 2-generator subsemigroups of $2\times 2$ matrices

2011-04-27

arxiv.org/abs/1104.5054v1

Mathematics

Number Theory

15 pages

Scientific paper

We show that the semigroup of real linear fractional transformations on a proper subinterval of the real line does not admit any 2-generator dense subsemigroups, and then we construct a 3-parameter family of examples of 3-generator dense subsemigroups. We also construct an explicit example of a 2-generator dense subsemigroup of $2\times 2$ real matrices. In the complex case, we prove the existence of uncountably many 2-generator dense subsemigroups.

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