The isotopy problem for Jordan matrix algebras
HTML articles powered by AMS MathViewer
- by Holger P. Petersson
- Trans. Amer. Math. Soc. 244 (1978), 185-197
- DOI: https://doi.org/10.1090/S0002-9947-1978-0506615-7
- PDF | Request permission
Abstract:
Conditions are given which are necessary and sufficient for two members of a certain class of Jordan matrix algebras to be isotopic. The main ingredient of these conditions is McCrimmon’s notion of isotopy for alternative algebras.References
- John R. Faulkner, Octonion planes defined by quadratic Jordan algebras, Memoirs of the American Mathematical Society, No. 104, American Mathematical Society, Providence, R.I., 1970. MR 0271180
- Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099, DOI 10.1090/coll/039
- N. Jacobson, Lectures on quadratic Jordan algebras, Tata Institute of Fundamental Research Lectures on Mathematics, No. 45, Tata Institute of Fundamental Research, Bombay, 1969. MR 0325715
- Ottmar Loos, Jordan pairs, Lecture Notes in Mathematics, Vol. 460, Springer-Verlag, Berlin-New York, 1975. MR 0444721, DOI 10.1007/BFb0080843
- Kevin McCrimmon, A general theory of Jordan rings, Proc. Nat. Acad. Sci. U.S.A. 56 (1966), 1072–1079. MR 202783, DOI 10.1073/pnas.56.4.1072
- Kevin McCrimmon, Homotopes of alternative algebras, Math. Ann. 191 (1971), 253–262. MR 313344, DOI 10.1007/BF01350327
- H. P. Petersson, Conjugacy of idempotents in Jordan pairs, Comm. Algebra 6 (1978), no. 7, 673–715. MR 488049, DOI 10.1080/00927877808822264
- R. D. Schafer, Alternative algebras over an arbitrary field, Bull. Amer. Math. Soc. 49 (1943), 549–555. MR 8610, DOI 10.1090/S0002-9904-1943-07967-0
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 244 (1978), 185-197
- MSC: Primary 17C50; Secondary 17D05
- DOI: https://doi.org/10.1090/S0002-9947-1978-0506615-7
- MathSciNet review: 506615