Conjugacy classes of hyperbolic matrices in $\textrm {Sl}(n, \textbf {Z})$ and ideal classes in an order
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- by D. I. Wallace PDF
- Trans. Amer. Math. Soc. 283 (1984), 177-184 Request permission
Abstract:
A bijection is proved between $\operatorname {Sl} (n,{\mathbf {Z}})$-conjugacy classes of hyperbolic matrices with eigenvalues $\{ {\lambda _1}, \ldots ,{\lambda _n}\}$ which are units in an $n$-degree number field, and narrow ideal classes of the ring ${R_k} = {\mathbf {Z}}[{\lambda _i}]$. A bijection between $\operatorname {Gl} (n,{\mathbf {Z}})$-conjugacy classes and the wide ideal classes, which had been known, is repeated with a different proof.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 283 (1984), 177-184
- MSC: Primary 11F06; Secondary 11R80
- DOI: https://doi.org/10.1090/S0002-9947-1984-0735415-0
- MathSciNet review: 735415