On special linear characters of free groups of rank $n\geq 4$
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- by Alice Whittemore PDF
- Proc. Amer. Math. Soc. 40 (1973), 383-388 Request permission
Abstract:
Let ${F_n}$ be a free group of rank $n$. In a recent paper R. Horowitz has shown that for $n \leqq 3$ the ideal ${I_n}$ in the ring of special linear characters of ${F_n}$ consisting of those polynomials in the characters which vanish for all representations of ${F_n}$ by subgroups of $SL(2,C)$ is principal. In this paper the case $n = 4$ is investigated; it is shown that for $n > 3,{I_n}$ is not principal.References
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R. Fricke and F. Klein, Vorlesungen über die Theorie der automorphen Functionen. Vol. 1, Teubner, Leipzig, 1897.
- Robert D. Horowitz, Characters of free groups represented in the two-dimensional special linear group, Comm. Pure Appl. Math. 25 (1972), 635–649. MR 314993, DOI 10.1002/cpa.3160250602 W. Magnus, A. Karass and D. Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Pure and Appl. Math., vol. 13, Interscience, New York, 1966. MR 34 #7617.
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 383-388
- MSC: Primary 20E35
- DOI: https://doi.org/10.1090/S0002-9939-1973-0322064-X
- MathSciNet review: 0322064