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Some free groups of matrices and the Burau representation of B4

Published online by Cambridge University Press:  24 October 2008

Siegfried Moran
Siegfried Moran
Affiliation:
The University, Canterbury, Kent
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Extract

Using a criterion due to J. Tits [4] we shall show that it is easy to give a pair of conjugate matrices in GLn(ℂ) which freely generate a free group of rank two. The difficulty lies in producing two such matrices whose freeness does not follow directly from the known freeness of two 2 × 2 matrices. Finally we show that the well known problem as to whether the Burau representation of Artin's braid group B4 is faithful turns out to be arbitrarily close to being true in a large number of ways. Thanks are due to the referee for his helpful comments.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 2 , September 1991 , pp. 225 - 228
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

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