Murray Gerstenhaber
Murray Gerstenhaber ( born June 5, 1927 in Brooklyn ) is an American mathematician who deals with algebra.
Life and work
Gerstenhaber was gifted early and went from 1940 to the Bronx High School of Science. After military service from 1945 to 1947 in the infantry, he went to Yale University, his undergraduate degree where he graduated in mathematics in 1948. In 1947 he won with the Yale team ( which also Murray Gell-Mann was ) the second prize in the William Lowell Putnam Competition -. In 1949 he received his master's degree at the University of Chicago and was there in 1951 with Abraham Adrian Albert doctorate ( Rings of Derivations ). As a post - graduate student, he was 1951/52, Frank D. Jewett Fellow at Harvard University and 1952/53, the Institute for Advanced Study. After that, he was at the University of Pennsylvania, first in 1953 as an assistant professor, in 1958 as an associate professor and from 1961 as a professor. 1982/83 he was chairman of the Faculty Senate of the University. He was repeatedly at the Institute for Advanced Study ( 1952-1953, 1957-1959, 1962, 1965/66, 1981/82 ) and 1961/62 at the Institute for Defense Analyses. 1990, he served as a guest speaker at the dedication of the Euler Institute in St. Petersburg.
He dealt with algebraic deformation theory, which he founded in the 1960s. In 1963 he led Gerstenhaber algebras as an algebraic structure ( graded with a commutative product and a graded Lie algebra ) on the Hochschild cohomology, which describes the deformation of algebras. They later found applications for example in quantum field theory ( Batalin - Vilkovisky formalism in gauge theories ) and Deformierungs quantization (including Moshe Flato, Daniel Sternheimer ) in the transition from classical physics to quantum mechanics and is another example of Gerstenhaber algebras is an outer product of a Lie algebra. He also dealt with mathematical problems of biology, which he brought out several anthologies in the 1960s and 1970s.
Besides his work as a professor of mathematics, he earned his doctorate in 1973 at the University of Pennsylvania Law ( JD, Juris Doctor), is marketed in Pennsylvania since 1974 as an attorney and taught at the Law School of the University of Pennsylvania. Gerstenhaber also dealt with the application of statistics and probabilistic conclusions on legal issues.
1965 to 1971 he was editor of the Bulletin of the American Mathematical Society. He is a Fellow of the American Mathematical Society.
He has been married since 1958 and has two sons and a daughter.
Writings
- On the deformation of rings and algebras, Annals of Mathematics, Volume 79, 1964, p 59-103, Part II, Volume 84, 1966, pp. 1-19, Part III, Volume 88, 1968, p.1 -34, Part IV, Volume 99, 1974, p 257-276, Part V with C. Wilkerson in Contemporary Mathematics, volume 227, 1999, p.89 -101
- With M. Hazewinkel deformation theory of Algebras and Structures and Applications, NATO ASI Series C, Vol 247, Kluwer, 1988 ( in Algebraic Cohomology and Deformation with Schack Theory, pp. 11-264 )
- With Jim Stasheff (Editor ) Deformation theory and quantum groups with applications to Mathematical Physics Contemporary Mathematics, Volume 134, 1992 ( in Samuel D. Schack Algebras, Bialgebras, Quantum Groups and algebraic deformation, p.51 -92)
- P. Bonneau, A. Giaquinto, Daniel Sternheimer quantum groups and deformation quantization: explicit and implicit aspects Approaches, J. Math Phys, Vol 45, 2004, pp. 3703-3741.