Higher-dimensional analogues of the modular and Picard groups

Higher-dimensional analogues of the modular and Picard groups
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by C. Maclachlan, P. L. Waterman and N. J. Wielenberg PDF

Trans. Amer. Math. Soc. 312 (1989), 739-753 Request permission

Clifford algebras are used to describe arithmetic groups which are generalizations of the modular and Picard groups.

References

Lars V. Ahlfors, On the fixed points of Möbius transformations in $\textbf {R}^n$, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 15–27. MR 802464, DOI 10.5186/aasfm.1985.1005
Lars V. Ahlfors, Möbius transformations and Clifford numbers, Differential geometry and complex analysis, Springer, Berlin, 1985, pp. 65–73. MR 780036
Armand Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485–535. MR 147566, DOI 10.2307/1970210
Andrew M. Brunner, Youn W. Lee, and Norbert J. Wielenberg, Polyhedral groups and graph amalgamation products, Topology Appl. 20 (1985), no. 3, 289–304. MR 804041, DOI 10.1016/0166-8641(85)90096-3

A language for group theory

H. S. M. Coxeter, Regular polytopes, 3rd ed., Dover Publications, Inc., New York, 1973. MR 0370327
H. S. M. Coxeter and W. O. J. Moser, Generators and relations for discrete groups, 4th ed., Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 14, Springer-Verlag, Berlin-New York, 1980. MR 562913, DOI 10.1007/978-3-662-21943-0
Leon Greenberg, Discrete subgroups of the Lorentz group, Math. Scand. 10 (1962), 85–107. MR 141731, DOI 10.7146/math.scand.a-10515

Discrete subgroup of Lie groups

I. N. Herstein, Topics in algebra, 2nd ed., Xerox College Publishing, Lexington, Mass.-Toronto, Ont., 1975. MR 0356988

Non-euclidean tesselations and their groups

Peter J. Nicholls, The minima of indefinite binary quadratic forms, J. Number Theory 16 (1983), no. 1, 19–30. MR 693391, DOI 10.1016/0022-314X(83)90029-X
Ian R. Porteous, Topological geometry, Van Nostrand Reinhold Co., London-New York-Melbourne, 1969. MR 0254852

The geometry and topology of

manifolds

Marie-France Vignéras, Arithmétique des algèbres de quaternions, Lecture Notes in Mathematics, vol. 800, Springer, Berlin, 1980 (French). MR 580949, DOI 10.1007/BFb0091027
È. B. Vinberg, Absence of crystallographic groups of reflections in Lobachevskiĭ spaces of large dimension, Trudy Moskov. Mat. Obshch. 47 (1984), 68–102, 246 (Russian). MR 774946
Robert J. Zimmer, Ergodic theory and semisimple groups, Monographs in Mathematics, vol. 81, Birkhäuser Verlag, Basel, 1984. MR 776417, DOI 10.1007/978-1-4684-9488-4