Free subgroups of quaternion algebras
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- by Roger C. Alperin
- Proc. Amer. Math. Soc. 118 (1993), 15-17
- DOI: https://doi.org/10.1090/S0002-9939-1993-1123646-0
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Abstract:
Using the theory of group actions on trees, we shall prove that if a quaternion algebra over Laurant polynomials is not split then a certain congruence subgroup of the group of norm one elements is a free group. This generalizes and gives an easy, conceptually simpler proof than that given by Pollen for the field of real numbers.References
- T. Y. Lam, The algebraic theory of quadratic forms, Mathematics Lecture Note Series, W. A. Benjamin, Inc., Reading, Mass., 1973. MR 0396410
- David Pollen, $\textrm {SU}_I(2,F[z,1/z])$ for $F$ a subfield of $\textbf {C}$, J. Amer. Math. Soc. 3 (1990), no. 3, 611–624. MR 1040953, DOI 10.1090/S0894-0347-1990-1040953-6
- Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. MR 607504
Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 15-17
- MSC: Primary 20E08; Secondary 57M07
- DOI: https://doi.org/10.1090/S0002-9939-1993-1123646-0
- MathSciNet review: 1123646