Bulletin of the American Mathematical Society
- Bull. Amer. Math. Soc.
- Volume 84, Number 4 (1978), 612-627.
Jordan algebras and their applications
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Article information
Source
Bull. Amer. Math. Soc., Volume 84, Number 4 (1978), 612-627.
Dates
First available in Project Euclid: 4 July 2007
Permanent link to this document
https://projecteuclid.org/euclid.bams/1183540925
Mathematical Reviews number (MathSciNet)
MR0466235
Zentralblatt MATH identifier
0421.17010
Subjects
Primary: 17Cxx: Jordan algebras (algebras, triples and pairs) 17B25: Exceptional (super)algebras 17B60: Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50] 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]
Citation
Mccrimmon, Kevin. Jordan algebras and their applications. Bull. Amer. Math. Soc. 84 (1978), no. 4, 612--627. https://projecteuclid.org/euclid.bams/1183540925
References
- 1. A. A. Albert, On a certain algebra of quantum mechanics, Ann. of Math. (2) 35 (1934), 65-73.
- 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.
- 4. P. M. Cohn, On homomorphic images of special Jordan algebras, Canad. J. Math. 6 (1954), 253-264.Zentralblatt MATH: 0055.02704
Mathematical Reviews (MathSciNet): MR60496
Digital Object Identifier: doi:10.4153/CJM-1954-026-9 - 5. P. M. Cohn, Free rings and their relations, Academic Press, New York, 1971.
- 6. J. Faulkner, Octonion planes defined by quadratic Jordan algebras, Mem. Amer. Math. Soc. No. 104 (1970).
- 7. F. Gürsey, Algebraic methods and quark structure, Proc. Kyoto Conf. on Math. Prob. in Theoretical Phys. 1975.Mathematical Reviews (MathSciNet): MR672960
- 8. S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962.
- 9. L. K. Hua, On semihomomorphisms of rings and their applications in projective geometry, Uspehi Mat. Nauk 8 (1953), no. 3 (53), 143-148.Mathematical Reviews (MathSciNet): MR58582
- 10. N. Jacobson, Structure and representations of Jordan algebras, Amer. Math. Soc. Colloq. Publ., vol. 39, Amer. Math. Soc., Providence, R.I., 1969.
- 11. N. Jacobson, Lectures on quadratic Jordan algebras, Tata Institute Lecture Notes, Bombay, 1969.
- 12. N. Jacobson, Structure theory for a class of Jordan algebras, Proc. Nat. Acad. Sci. U. S. A. 55 (1966), 243-251.Zentralblatt MATH: 0133.28903
Mathematical Reviews (MathSciNet): MR193116
Digital Object Identifier: doi:10.1073/pnas.55.2.243 - 13. N. Jacobson, Exceptional Lie algebras, Dekker, New York, 1971.
- 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.
- 15. V. Kac, Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras (to appear).Zentralblatt MATH: 0367.17007
Mathematical Reviews (MathSciNet): MR498755
Digital Object Identifier: doi:10.1080/00927877708822224 - 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.
- 18. M. Koecher, Jordan algebras and their applications, Univ. Minnesota Lecture Notes, Minneapolis, 1962.Zentralblatt MATH: 0128.03101
- 19. M. Koecher, An elementary approach to bounded symmetric domains, Rice Univ. Lecture Notes, Houston, 1969.
- 20. O. Loos, Jordan pairs, Lecture Notes in Math., vol. 460, Springer-Verlag, New York, 1975.
- 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.Zentralblatt MATH: 0229.17002
Mathematical Reviews (MathSciNet): MR310024
Digital Object Identifier: doi:10.1090/S0002-9947-1971-0310024-7 - 23. K. McCrimmon, A general theory of Jordan rings, Proc. Nat. Acad. Sci. U. S. A. 56 (1966), 1072-1079.Zentralblatt MATH: 0139.25502
Mathematical Reviews (MathSciNet): MR202783
Digital Object Identifier: doi:10.1073/pnas.56.4.1072 - 24. K. McCrimmon, Jordan algebras with interconnected idempotents, Proc. Amer. Math. Soc. 19 (1968) 1327-1336.Zentralblatt MATH: 0174.06602
Mathematical Reviews (MathSciNet): MR231875
Digital Object Identifier: doi:10.1090/S0002-9939-1968-0231875-9 - 25. K. McCrimmon, Axioms for inversion in Jordan algebras, J. Algebra 47 (1977).Zentralblatt MATH: 0421.17013
Mathematical Reviews (MathSciNet): MR470002
Digital Object Identifier: doi:10.1016/0021-8693(77)90221-6 - 26. K. McCrimmon, On Herstein's theorems relating Jordan and associative algebras, J. Algebra 13 (1969), 382-392.Zentralblatt MATH: 0224.16027
Mathematical Reviews (MathSciNet): MR249476
Digital Object Identifier: doi:10.1016/0021-8693(69)90081-7 - 27. R. Moufang, Alternative körper und der Satz vom Vollständigen Vierseit, Abh. Math. Sem. Univ. Hamburg 9 (1933), 207-222.Zentralblatt MATH: 0007.07205
- 28. J. von Neumann, On an algebraic generalization of the quantum mechanical formalism, Mat. Sb. 1 (1936), 415-482.Zentralblatt MATH: 0015.24505
- 29. T. A. Springer, Jordan algebras and algebraic groups, Springer-Verlag, New York, 1973.
- 30. T. A. Springer, The projective octave plane, Indag. Math. 22 (1960), 74-101.
- 31. A. Thedy, Right alternative rings, J. Algebra 37 (1975), 1-63.Zentralblatt MATH: 0318.17011
Mathematical Reviews (MathSciNet): MR384888
Digital Object Identifier: doi:10.1016/0021-8693(75)90086-1 - 32. J. Tits, Algèbres alternatives, algèbres de Jordan, et algèbres de Lie exceptionelles. I, Indag. Math. 28 (1966), 223-237.
- 33. D. M. Topping, Jordan algebras of selfadjoint operators, Mem. Amer. Math. Soc. No. 53 (1965).
- 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.
- 35. W. Kaup, Algebraic characterization of symmetric complex Banach manifolds, Math. Ann, (to appear).Zentralblatt MATH: 0335.58005
Mathematical Reviews (MathSciNet): MR454091
Digital Object Identifier: doi:10.1007/BF01360772 - 36. M. Koecher, Jordan algebras in differential geometry, Proc. Internat. Congress I, (Nice, 1970), 279-283.
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