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Jordan algebras and their applications
Author:
Kevin Mccrimmon
Journal:
Bull. Amer. Math. Soc. 84 (1978), 612-627
MSC (1970):
Primary 17Cxx, 17B25, 17B60, 32M15
MathSciNet review:
0466235
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References |
Similar Articles |
Additional Information
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McCrimmon, Axioms for inversion in Jordan algebras, J. Algebra
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Kevin
McCrimmon, On Herstein’s theorems relating Jordan and
associative algebras, J. Algebra 13 (1969),
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R. Moufang, Alternative körper und der Satz vom Vollständigen Vierseit, Abh. Math. Sem. Univ. Hamburg 9 (1933), 207-222.
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Wilhelm
Kaup, Algebraic characterization of symmetric complex Banach
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39–64. MR
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- 36.
Max
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Congrès International des Mathématiciens (Nice, 1970)
Gauthier-Villars, Paris, 1971, pp. 279–283. MR 0430013
(55 #3021)
- 1.
- A. A. Albert, On a certain algebra of quantum mechanics, Ann. of Math. (2) 35 (1934), 65-73. MR 1503142
- 2.
- E. Alfsen, F. Schultz and E. Störmer, A Gelfand-Neumark theorem for Jordan algebras (to appear).
- 3.
- H. Braun and M. Koecher, Jordan Algebren, Springer-Verlag, Berlin, 1966. MR 204470
- 4.
- P. M. Cohn, On homomorphic images of special Jordan algebras, Canad. J. Math. 6 (1954), 253-264. MR 60496
- 5.
- P. M. Cohn, Free rings and their relations, Academic Press, New York, 1971. MR 371938
- 6.
- J. Faulkner, Octonion planes defined by quadratic Jordan algebras, Mem. Amer. Math. Soc. No. 104 (1970). MR 271180
- 7.
- F. Gürsey, Algebraic methods and quark structure, Proc. Kyoto Conf. on Math. Prob. in Theoretical Phys. 1975. MR 672960
- 8.
- S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962. MR 145455
- 9.
- L. K. Hua, On semihomomorphisms of rings and their applications in projective geometry, Uspehi Mat. Nauk 8 (1953), no. 3 (53), 143-148. MR 58582
- 10.
- N. Jacobson, Structure and representations of Jordan algebras, Amer. Math. Soc. Colloq. Publ., vol. 39, Amer. Math. Soc., Providence, R.I., 1969. MR 251099
- 11.
- N. Jacobson, Lectures on quadratic Jordan algebras, Tata Institute Lecture Notes, Bombay, 1969. MR 325715
- 12.
- N. Jacobson, Structure theory for a class of Jordan algebras, Proc. Nat. Acad. Sci. U. S. A. 55 (1966), 243-251. MR 193116
- 13.
- N. Jacobson, Exceptional Lie algebras, Dekker, New York, 1971. MR 284482
- 14.
- P. Jordan, J. von Neumann and E. Wigner, On an algebraic generalization of the quantum mechanical formalism, Ann. of Math. (2) 36 (1934), 29-64. MR 1503141
- 15.
- V. Kac, Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras (to appear). MR 498755
- 16.
- J. Kaplansky, Graded Lie and Jordan algebras (to appear).
- 17.
- M. Koecher, On Lie algebras defined by Jordan algebras, Aarhus Univ. Lecture Notes, Aarhus, 1967. MR 257162
- 18.
- M. Koecher, Jordan algebras and their applications, Univ. Minnesota Lecture Notes, Minneapolis, 1962.
- 19.
- M. Koecher, An elementary approach to bounded symmetric domains, Rice Univ. Lecture Notes, Houston, 1969. MR 261032
- 20.
- O. Loos, Jordan pairs, Lecture Notes in Math., vol. 460, Springer-Verlag, New York, 1975. MR 444721
- 21.
- O. Loos, Jordan pairs and bounded symmetric domains, Lecture Notes, Univ. of California at Irvine, 1977.
- 22.
- K. McCrimmon, Noncommutative Jordan rings, Trans. Amer. Math. Soc. 158 (1971), 1-33. MR 310024
- 23.
- K. McCrimmon, A general theory of Jordan rings, Proc. Nat. Acad. Sci. U. S. A. 56 (1966), 1072-1079. MR 202783
- 24.
- K. McCrimmon, Jordan algebras with interconnected idempotents, Proc. Amer. Math. Soc. 19 (1968) 1327-1336. MR 231875
- 25.
- K. McCrimmon, Axioms for inversion in Jordan algebras, J. Algebra 47 (1977). MR 470002
- 26.
- K. McCrimmon, On Herstein's theorems relating Jordan and associative algebras, J. Algebra 13 (1969), 382-392. MR 249476
- 27.
- R. Moufang, Alternative körper und der Satz vom Vollständigen Vierseit, Abh. Math. Sem. Univ. Hamburg 9 (1933), 207-222.
- 28.
- J. von Neumann, On an algebraic generalization of the quantum mechanical formalism, Mat. Sb. 1 (1936), 415-482.
- 29.
- T. A. Springer, Jordan algebras and algebraic groups, Springer-Verlag, New York, 1973. MR 379618
- 30.
- T. A. Springer, The projective octave plane, Indag. Math. 22 (1960), 74-101. MR 126196
- 31.
- A. Thedy, Right alternative rings, J. Algebra 37 (1975), 1-63. MR 384888
- 32.
- J. Tits, Algèbres alternatives, algèbres de Jordan, et algèbres de Lie exceptionelles. I, Indag. Math. 28 (1966), 223-237. MR 219578
- 33.
- D. M. Topping, Jordan algebras of selfadjoint operators, Mem. Amer. Math. Soc. No. 53 (1965). MR 190788
- 34.
- L. Harris, Bounded symmetric homogeneous domains in infinite dimensional spaces, Proc. Infinite Dimensional Holomorphy, Lecture Notes in Math., vol. 364, Springer-Verlag, New York, 1974. MR 407330
- 35.
- W. Kaup, Algebraic characterization of symmetric complex Banach manifolds, Math. Ann, (to appear). MR 454091
- 36.
- M. Koecher, Jordan algebras in differential geometry, Proc. Internat. Congress I, (Nice, 1970), 279-283. MR 430013
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1978-14503-0
PII:
S 0002-9904(1978)14503-0
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