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Transactions of the American Mathematical Society

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Conjugacy classes of hyperbolic matrices in $ {\rm Sl}(n,\,{\bf Z})$ and ideal classes in an order

Author: D. I. Wallace
Journal: Trans. Amer. Math. Soc. 283 (1984), 177-184
MSC: Primary 11F06; Secondary 11R80
MathSciNet review: 735415
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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.

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Article copyright: © Copyright 1984 American Mathematical Society