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Discrete Arithmetic Groups

  • Colin Maclachlan
  • Alan W. Reid
Part of the Graduate Texts in Mathematics book series (GTM, volume 219)

Abstract

The description of arithmetic Kleinian groups and arithmetic Fuchsian groups via quaternion algebras and their orders is convenient, as it links up with the earlier use of quaternion algebras and number fields as commensurability invariants of general Kleinian groups. This description also clarifies the connections between the arithmetic, on the one hand, and the topological, geometric and group-theoretic properties of the groups, on the other. This has been illustrated in Chapter 9 and further aspects will be pursued in the remaining chapters.

Keywords

Algebraic Group Number Field Clifford Algebra Orthogonal Group Kleinian Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Further Reading

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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Colin Maclachlan
    • 1
  • Alan W. Reid
    • 2
  1. 1.Department of Mathematical Sciences, Kings CollegeUniversity of AberdeenAberdeenUK
  2. 2.Department of MathematicsUniversity of Texas at AustinAustinUSA

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