Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Jordan algebras and their applications


Author: Kevin Mccrimmon
Journal: Bull. Amer. Math. Soc. 84 (1978), 612-627
MSC (1970): Primary 17Cxx, 17B25, 17B60, 32M15
DOI: https://doi.org/10.1090/S0002-9904-1978-14503-0
MathSciNet review: 0466235
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. A. Adrian Albert, On a certain algebra of quantum mechanics, Ann. of Math. (2) 35 (1934), no. 1, 65–73. MR 1503142, https://doi.org/10.2307/1968118
  • 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) 35 (1934), no. 1, 29–64. MR 1503141, https://doi.org/10.2307/1968117
  • 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

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 17Cxx, 17B25, 17B60, 32M15

Retrieve articles in all journals with MSC (1970): 17Cxx, 17B25, 17B60, 32M15


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1978-14503-0

American Mathematical Society