Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Conjugacy classes of symmetries
in orthogonal groups

Author: Donald G. James
Journal: Proc. Amer. Math. Soc. 125 (1997), 747-753
MSC (1991): Primary 11E57, 11F06, 20G30
MathSciNet review: 1416090
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The number of conjugacy classes of symmetries in the integral orthogonal group of an indefinite $\Bbb Z$-lattice is determined. The results are applied to the extended Bianchi groups.

References [Enhancements On Off] (What's this?)

  • 1. A.G. Earnest and J.S. Hsia, Spinor norms of local integral rotations II, Pacific J. Math. 61 (1975), 71-86. MR 85m:11022
  • 2. J. Elstrodt, F. Grunewald and J. Mennicke, Discontinuous groups on three-dimensional hyperbolic space: analytical theory and arithmetic applications, Russian Math. Surveys 38 (1983), 137-168. MR 85g:11045
  • 3. A.J. Hahn and O.T. O'Meara, The Classical Groups and $K$-Theory, Springer-Verlag (1989). MR 90i:20002
  • 4. D.G. James, Representations by integral quadratic forms, J. Number Theory 4 (1972), 321-329. MR 46:8976
  • 5. D.G. James, Integral sums of squares in algebraic number fields, Amer. J. Math. 113 (1991), 129-146. MR 92j:11036
  • 6. D.G. James and C. Maclachlan, Fuchsian subgroups of Bianchi groups, Trans. Amer. Math. Soc. 348 (1996), 1989-2002. CMP 96:09
  • 7. D.G. James and S.M. Rosenzweig, Associated vectors in lattices over valuation rings, Amer. J. Math. 90 (1968), 295-307. MR 36:3754
  • 8. O.T. O'Meara, Introduction to Quadratic Forms, Springer-Verlag (1963). MR 27:2485
  • 9. A. Trojan, The integral extension of isometries of quadratic forms over local fields, Canadian J. Math. 18 (1966), 920-942. MR 34:2561
  • 10. E.B. Vinberg, Reflective subgroups in Bianchi groups, Selecta Math. Sov. 9 (1990), 309-314. MR 91j:20117
  • 11. L.Va. Vulakh, Reflections in extended Bianchi groups, Math. Proc. Camb. Phil. Soc. 115 (1994), 13-25. MR 94k:20086

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 11E57, 11F06, 20G30

Retrieve articles in all journals with MSC (1991): 11E57, 11F06, 20G30

Additional Information

Donald G. James

Received by editor(s): October 18, 1995
Additional Notes: The author was supported by NSA grant MDA904-94-H-2034 and NSF grant DMS-95-00533.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society