Moss Eisenberg Sweedler (born 29 April 1942, in

Brooklyn Brooklyn () is a borough of New York City, coextensive with Kings County, in the U.S. state of New York. Kings County is the most populous county in the State of New York, and the second-most densely populated county in the United States, be ...

) is an American mathematician, known for

Sweedler's Hopf algebra In mathematics, introduced an example of an infinite-dimensional Hopf algebra, and Sweedler's Hopf algebra ''H''4 is a certain 4-dimensional quotient of it that is neither commutative nor cocommutative. Definition The following infinite dimen ...

, Sweedler's notation,

measuring coalgebra In algebra, a measuring coalgebra of two algebras ''A'' and ''B'' is a coalgebra In mathematics, coalgebras or cogebras are structures that are dual (in the category-theoretic sense of reversing arrows) to unital associative algebras. The axioms ...

s, and his proof, with Harry Prince Allen, of a conjecture of

Nathan Jacobson Nathan Jacobson (October 5, 1910 – December 5, 1999) was an American mathematician. Biography Born Nachman Arbiser in Warsaw, Jacobson emigrated to America with his family in 1918. He graduated from the University of Alabama in 1930 and was awar ...

Education and career

Sweedler received his Ph.D. from the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

in 1965. His thesis, ''Commutative Hopf Algebras with Antipode,'' was written under the direction of thesis advisor

Bertram Kostant Bertram Kostant (May 24, 1928 – February 2, 2017) was an American mathematician who worked in representation theory, differential geometry, and mathematical physics. Early life and education Kostant grew up in New York City, where he gradua ...

. Sweedler wrote ''Hopf Algebras'' (1969), which became the standard reference book on Hopf algebras. He, with Harry P. Allen, used Hopf algebras to prove in 1969 a famous 25-year-old conjecture of Jacobson about the forms of generalized Witt algebras over algebraically closed fields of finite characteristic. From 1965 to the mid 1980s Sweeder worked on commutative algebra and related disciplines.Moss E. Sweedler, www.math.cornell.edu
/ref> Since the mid 1980s Sweedler has worked primarily on

computer algebra In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions ...

. His research resulted in his position as director of the Army Center of Excellence for computer algebra. Sweedler was an Invited Speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in 1974 in Vancouver. He was a Guggenheim Fellow for the academic year 1980–1981. With his wife Kristin, he helped establish the Sweedler Nature Preserve.Lick Brook Falls @ Sweedler Nature Preserve
/ref>

Selected publications

* * * * *with H. P. Allen: *with Richard G. Larson: * *Groups of simple algebras, Institut des Hautes Etudes Scientifiques 44 (1975), 79–189. * * *with Kenneth Newman: *with Darrell E. Halle and R. Larson: *with I. Rubio and C. Heegard: Gröbner bases for linear recursion relations on m-D arrays and applications to decoding, Proc. IEEE Int'l Symp. on Information Theory, June 29–July 4, 1997, Ulm, Germany. *with K. Shirayanagi: Remarks on automatic algorithm stabilization, invited contribution to (fourth) IMACS Conf. on Appl. of Computer Algebra (1998). *with L. Robbiano: *with Edward Mosteig:

References

20th-century American mathematicians 21st-century American mathematicians Massachusetts Institute of Technology School of Science alumni Cornell University faculty 1942 births Living people Algebraists {{US-mathematician-stub