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Book Review
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Book Information
Author(s):
John H. Conway and Derek A. Smith
Title:
On quaternions and octonions: Their geometry, arithmetic, and symmetry
Additional book information:
A K Peters, Ltd.,
Natick, MA,
2003,
xii + 159,
$29.00,
1-56881-134-9
References:
-
- 1.
- J. F. Adams, Lectures on Lie Groups, Benjamin, New York, 1969. MR 0252560 (40:5780)
- 2.
- J. F. Adams, Lectures on Exceptional Lie Groups, eds. Z. Mahmud and M. Mimira, University of Chicago Press, Chicago, 1996. MR 1428422 (98b:22001)
- 3.
- J. C. Baez, The octonions, Bull. Amer. Math. Soc. 39 (2002), 145-205. MR 1886087 (2003f:17003) Corrected version available at math.RA/0105155.
- 4.
- J. W. S. Cassels, An Introduction to the Geometry of Numbers, Springer, Berlin, 1997. MR 1434478 (97i:11074)
- 5.
- J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 2nd edition, Springer, Berlin, 1993. MR 1194619 (93h:11069)
- 6.
- H. S. M. Coxeter, Integral Cayley numbers, Duke Math. Jour. 13 (1946), 561-578. MR 0019111 (8:370b)
- 7.
- M. J. Crowe, A History of Vector Analysis, University of Notre Dame Press, Notre Dame, 1967. MR 0229496 (37:5070)
- 8.
- D. D. Fenster, Leonard Eugene Dickson and his work in the arithmetics of algebras, Arch. Hist. Exact Sci. 52 (1998), 119-159. MR 1610132 (99e:01020)
- 9.
- Hans Freudenthal, Beziehungen der
und zur Oktavenebene, I, II, Indag. Math. 16 (1954), 218-230, 363-368. III, IV, Indag. Math. 17 (1955), 151-157, 277-285. V -- IX, Indag. Math. 21 (1959), 165-201, 447-474. X, XI, Indag. Math. 25 (1963) 457-487. MR 0063358 (16:108b), MR 0068549 (16:900d), MR 0068550 (16:900e), MR 0068551 (16:900f), MR 163203 (29:506) - 10.
- W. Fulton and J. Harris, Representation Theory -- a First Course, Springer, Berlin, 1991. MR 1153249 (93a:20069)
- 11.
- P. M. Gruber and C. G. Lekkerkerker, Geometry of Numbers, second edition, North-Holland, New York, 1987. MR 0893813 (88j:11034)
- 12.
- M. Gunaydin, K. Koepsell and H. Nicolai, Conformal and quasiconformal realizations of exceptional Lie groups, Comm. Math. Phys. 221 (2001), 57-76. MR 1846901 (2002h:22019) Also available as hep-th/0008063.
- 13.
- S. Kaneyuki, Graded Lie algebras, related geometric structures, and pseudo-hermitian symmetric spaces, in Analysis and Geometry on Complex Homogeneous Domains, by Faraut, Kaneyuki, Koranyi, Lu, and Roos, Birkhäuser, New York, 2000. MR 1727259 (2001f:32036)
- 14.
- T. A. Larsson, Structures preserved by exceptional Lie algebras, available as math-ph/0301006.
- 15.
- K. McCrimmon, Jordan algebras and their applications, Bull. Amer. Math. Soc. 84 (1978), 612-627. MR 0466235 (57:6115)
- 16.
- C. L. Siegel, Lectures on the Geometry of Numbers, Springer, Berlin, 1989. MR 1020761 (91d:11070)
- 17.
- T. A. Springer and F. D. Veldkamp, Octonions, Jordan Algebras and Exceptional Groups, Springer, Berlin, 2000. MR 1763974 (2001f:17006)
- 18.
- M. Waldschmidt, P. Moussa, J.-M. Luck, and C. Itzykson, eds., From Number Theory to Physics, Springer, Berlin, 1992. MR 1221099 (93m:11001)
Additional Information:
Reviewer(s):
John
C.
Baez
Affiliation:
University of California, Riverside
Email:
baez@math.ucr.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
42
(2005),
229-243.
MSC
(2000):
Primary 11H31, 17-01, 17A35;
Secondary 17C40, 22E46, 52B11
DOI:
10.1090/S0273-0979-05-01043-8
PII:
S 0273-0979(05)01043-8
Posted:
January 26, 2005
Copyright of article:
Copyright
2005,
John C. Baez
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