Bulletin of the American Mathematical Society

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Book Information:

Authors: 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 pp., ISBN 1-56881-134-9, $29.00$

J. Frank Adams, Lectures on Lie groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0252560

J. F. Adams, Lectures on exceptional Lie groups, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1996. With a foreword by J. Peter May; Edited by Zafer Mahmud and Mamoru Mimura. MR 1428422

John C. Baez, The octonions, Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 2, 145–205. MR 1886087, DOI 10.1090/S0273-0979-01-00934-X

J. W. S. Cassels, An introduction to the geometry of numbers, Classics in Mathematics, Springer-Verlag, Berlin, 1997. Corrected reprint of the 1971 edition. MR 1434478

J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 290, Springer-Verlag, New York, 1993. With additional contributions by E. Bannai, R. E. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. MR 1194619, DOI 10.1007/978-1-4757-2249-9

H. S. M. Coxeter, Integral Cayley numbers, Duke Math. J. 13 (1946), 561–578. MR 19111

Michael J. Crowe, A history of vector analysis. The evolution of the idea of a vectorial system, University of Notre Dame Press, Notre Dame, Ind.-London, 1967. MR 0229496

Della Dumbaugh Fenster, Leonard Eugene Dickson and his work in the arithmetics of algebras, Arch. Hist. Exact Sci. 52 (1998), no. 2, 119–159. MR 1610132, DOI 10.1007/s004070050014

Hans Freudenthal, Beziehungen der $E_7$ und $E_8$ zur Oktavenebene. I, Nederl. Akad. Wetensch. Proc. Ser. A. 57 = Indagationes Math. 16 (1954), 218–230 (German). MR 0063358

William Fulton and Joe Harris, Representation theory, Graduate Texts in Mathematics, vol. 129, Springer-Verlag, New York, 1991. A first course; Readings in Mathematics. MR 1153249, DOI 10.1007/978-1-4612-0979-9

P. M. Gruber and C. G. Lekkerkerker, Geometry of numbers, 2nd ed., North-Holland Mathematical Library, vol. 37, North-Holland Publishing Co., Amsterdam, 1987. MR 893813

M. Günaydin, K. Koepsell, and H. Nicolai, Conformal and quasiconformal realizations of exceptional Lie groups, Comm. Math. Phys. 221 (2001), no. 1, 57–76. MR 1846901, DOI 10.1007/PL00005574

Jacques Faraut, Soji Kaneyuki, Adam Korányi, Qi-keng Lu, and Guy Roos, Analysis and geometry on complex homogeneous domains, Progress in Mathematics, vol. 185, Birkhäuser Boston, Inc., Boston, MA, 2000. MR 1727259, DOI 10.1007/978-1-4612-1366-6

14.

T. A. Larsson, Structures preserved by exceptional Lie algebras, available as math-ph/0301006.

Kevin McCrimmon, Jordan algebras and their applications, Bull. Amer. Math. Soc. 84 (1978), no. 4, 612–627. MR 466235, DOI 10.1090/S0002-9904-1978-14503-0

Carl Ludwig Siegel, Lectures on the geometry of numbers, Springer-Verlag, Berlin, 1989. Notes by B. Friedman; Rewritten by Komaravolu Chandrasekharan with the assistance of Rudolf Suter; With a preface by Chandrasekharan. MR 1020761, DOI 10.1007/978-3-662-08287-4

Tonny A. Springer and Ferdinand D. Veldkamp, Octonions, Jordan algebras and exceptional groups, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2000. MR 1763974, DOI 10.1007/978-3-662-12622-6

M. Waldschmidt, P. Moussa, J. M. Luck, and C. Itzykson (eds.), From number theory to physics, Springer-Verlag, Berlin, 1992. Papers from the Meeting on Number Theory and Physics held in Les Houches, March 7–16, 1989. MR 1221099, DOI 10.1007/978-3-662-02838-4

1.

J. F. Adams, Lectures on Lie Groups, Benjamin, New York, 1969. MR 0252560

2.

J. F. Adams, Lectures on Exceptional Lie Groups, eds. Z. Mahmud and M. Mimira, University of Chicago Press, Chicago, 1996. MR 1428422

3.

J. C. Baez, The octonions, Bull. Amer. Math. Soc. 39 (2002), 145-205. MR 1886087 Corrected version available at math.RA/0105155.

4.

J. W. S. Cassels, An Introduction to the Geometry of Numbers, Springer, Berlin, 1997. MR 1434478

5.

J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 2nd edition, Springer, Berlin, 1993. MR 1194619

6.

H. S. M. Coxeter, Integral Cayley numbers, Duke Math. Jour. 13 (1946), 561-578. MR 0019111

7.

M. J. Crowe, A History of Vector Analysis, University of Notre Dame Press, Notre Dame, 1967. MR 0229496

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

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, MR 0068549 (16:900d), MR 0068550 (16:900e), MR 0068551, MR 163203 (29:506)

10.

W. Fulton and J. Harris, Representation Theory -- a First Course, Springer, Berlin, 1991. MR 1153249

11.

P. M. Gruber and C. G. Lekkerkerker, Geometry of Numbers, second edition, North-Holland, New York, 1987. MR 0893813

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 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

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

16.

C. L. Siegel, Lectures on the Geometry of Numbers, Springer, Berlin, 1989. MR 1020761

17.

T. A. Springer and F. D. Veldkamp, Octonions, Jordan Algebras and Exceptional Groups, Springer, Berlin, 2000. MR 1763974

18.

M. Waldschmidt, P. Moussa, J.-M. Luck, and C. Itzykson, eds., From Number Theory to Physics, Springer, Berlin, 1992. MR 1221099