Kevin McCrimmon

Kevin Mor McCrimmon (born September 1941) is an American mathematician, specializing in Jordan algebras. He is known for his introduction of quadratic Jordan algebras in 1966.

McCrimmon attended secondary school in Champaign-Urbana, Illinois and then received his bachelor's degree in mathematics in 1960 from Reed College in Portland, Oregon.[1] He received his Ph.D. from Yale University in 1965 with thesis Norms and Noncommutative Jordan Algebras supervised by Nathan Jacobson.[2] McCrimmon spent his final year as a graduate student at the University of Chicago,[1] when Nathan Jacobson spent a year of unpaid leave visiting Chicago and Japan for the academic year 1964–1965.[3] As a postdoc, McCrimmon was at Massachusetts Institute of Technology from 1965 to 1967, for one year as an Air Force Research Laboratory Postdoctoral Fellow and for the next year as a C. L. E. Moore instructor. He became in 1967 a member of the Center for Advanced Studies at the University of Virginia (UVA), in 1968 an associate professor at UVA, and in 1972, a full professor at UVA, retiring there as professor emeritus.[1] He was chair of the mathematics department from 1972 to 1975.[1]

McCrimmon was a Sloan Fellow in 1968 and an Invited Speaker of the International Congress of Mathematicians in 1974 in Vancouver.[4] He spent several years on sabbatical in Europe.[1] He was elected a Fellow of the American Mathematical Society in 2017.

Selected publications

• with Richard D. Schafer. "On a class of noncommutative Jordan algebras." Proceedings of the National Academy of Sciences 56, no. 1 (1966): 1–4. PMC 285663
• "A general theory of Jordan rings." Proceedings of the National Academy of Sciences of the United States of America 56, no. 4 (1966): 1072–1079. PMC 220000
• "The radical of a Jordan algebra." Proceedings of the National Academy of Sciences of the United States of America 62, no. 3 (1969): 671–678. PMC 223650
• "The Freudenthal-Springer-Tits constructions of exceptional Jordan algebras." Transactions of the American Mathematical Society 139 (1969): 495–510. doi:10.2307/1995337
• "On Herstein's theorems relating Jordan and associative algebras." Journal of Algebra 13, no. 3 (1969): 382–392. doi:10.1016/0021-8693(69)90081-7
• "Noncommutative Jordan rings." Transactions of the American Mathematical Society 158 (1971): 1–33. doi:10.1090/S0002-9947-1971-0310024-7
• "Inner ideals in quadratic Jordan algebras." Transactions of the American Mathematical Society 159 (1971): 445–468.
• "Jordan algebras and their applications." Bulletin of the American Mathematical Society 84, no. 4 (1978): 612–627. doi:10.1090/S0002-9904-1978-14503-0
• with Leslie Hogben: "Maximal modular inner ideals and the Jacobson radical of a Jordan algebra." Journal of Algebra 68, no. 1 (1981): 155–169. doi:10.1016/0021-8693(81)90291-X
• with Ephim Zel'manov: "The structure of strongly prime quadratic Jordan algebras." Advances in Mathematics 69, no. 2 (1988): 133–222. doi:10.1016/0001-8708(88)90001-1
• A taste of Jordan algebras. Springer Science & Business Media, 2006.[5][6][7]

References

1. "Kevin McCrimmon, Biographical Sketch". pi.math.virginia.edu/Faculty.
2. Kevin Mor McCrimmon at the Mathematics Genealogy Project
3. O'Connor, John J.; Robertson, Edmund F., "Nathan Jacobson", MacTutor History of Mathematics archive, University of St Andrews.
4. McCrimmon, Kevin. "Quadratic methods in nonassociative algebras." In International Congress of Mathematicians, Vancouver, 1974. Proceedings, vol. 1, pp. 325–330. 1975.
5. Bertram, Wolfgang (March 2005). "Review of A Taste of Jordan Algebras by Kevin McCrimmon" (PDF). SIAM Review. 47 (1): 172–174. JSTOR 20453611.
6. Berg, Michael (19 November 2004). "Joint review of Mathematical Foundations of Quantum Mechanics by George W. Mackey and A Taste of Jordan Algebras by Kevin McCrimmon". MAA Reviews, maa.org.
7. "A Taste of Jordan Algebras" by Kevin McCrimmon, bokus.com