Hans Julius Zassenhaus
Hans Julius Zassenhaus (born May 28, 1912 in Koblenz , † November 21, 1991 in Columbus , Ohio ) was a German mathematician , famous for his work on algebra and as a pioneer of computer algebra .
Life
Zassenhaus was a Rhinelander from Koblenz, but the family moved to Hamburg in 1916. He rejected his original wish to become a physicist and instead became a student of Erich Hecke and Emil Artin in Hamburg , where he wrote his doctoral thesis in 1934 with the title Characterization of finite linear groups as permutation groups . In it he introduced permutation groups , the " Zassenhaus groups ", which play an important role in the later classification of the finite simple groups (work by Suzuki and others). In the same year he published a new proof of the Jordan-Holder theorem in group theory (with a lemma named after him ). Schur-Zassenhaus's group theory theorem is also associated with his name. From 1934 to 1936 he was at the University of Rostock , where he wrote his group theory textbook, like van der Waerden in his algebra after lectures by Emil Artin . In 1936 he completed his habilitation as Artin's assistant in Hamburg with a thesis on Lierings about bodies with prime number characteristics (modular Lie algebras). During the Second World War he worked alongside his university work in the navy for weather forecasting (and not, as is actually obvious, in cryptography) and was involved in the resistance.
In 1943 he was offered a professorship in Bonn , which he refused - he asked that the decision be postponed “until after the war”. In 1948/49 he was in Glasgow, and then from 1949 to 1959 he was a professor at McGill University in Montreal . He then worked for five years at the University of Notre Dame and moved to Ohio State University in 1964 , where he stayed until his retirement .
He developed several algorithms in algebra and algebraic number theory (calculation of class groups, Galois groups , units, etc.). The Zassenhaus algorithm for determining the intersection and sum bases of two subspaces in linear algebra was named after him . He was a pioneer in the use of computers in the 1960s (partly in collaboration with Olga Taussky-Todd ).
He later returned several times to the theoretical physics he had initially studied , for example in a series of works with Jiří Patera and Pavel Winternitz on the subgroup structure in the physics of important Lie groups and in contributions to the colloquia Group theoretical methods in physics . He also worked on algorithms for the classification of crystallographic space groups (here, too, a Zassenhaus algorithm is named after him) and in the geometry of numbers. In the mathematical-historical field, he edited Hermann Minkowski's letters to David Hilbert and also wrote about the mathematical contrast between the two, although he saw himself more as a consequence of Minkowski. In various essays, Zassenhaus also thought about pedagogical issues.
In 1962 he gave a lecture at the International Congress of Mathematicians in Stockholm ( The Lie algebras with a non degenerate trace form , with Richard E. Block ). In 1969 he was the founding editor of the Journal of Number Theory .
He was the older brother of the doctor and author Hiltgunt Zassenhaus . Zassenhaus had been married since 1942 and had three children.
His mathematical legacy is kept in the Central Archives for Mathematicians' Legacies at the Göttingen University Library.
Fonts
- Textbook of group theory . Teubner, Leipzig 1937 (also English translation, first Chelsea Verlag, 1949)
- Lie algebras and representation theory . Montreal 1981
- with Michael Pohst : Algorithmic algebraic number theory . Cambridge 1997 (first 1989)
- Rubik's cube - a toy, a Galois tool, group theory for everybody . In: Physica A . Volume 114, 1982, p. 629
- About the constructive treatment of mathematical problems . Rhenish-Westphalian Academy of Sciences 1982
- On the Minkowski-Hilbert dialogue on mathematization . In: Canadian Math. Bull. Volume 18, 1975, p. 443
- How programming difficulties can lead to theoretical advances . In: Proc. Symp. Applied Mathematics . Volume 15, 1963, p. 87
- Experimental mathematics in research and teaching . In: Math. Physikal. Semester reports . Volume 13, 1965, p. 135
- Methods and problems of modern algebra . Annual report DMV 1994, No. 1
- About the fundamental constructions of finite body theory . In: Jb DMV 1968
- About the existence of prime numbers in arithmetic progressions . In: Comm.Math.Helvetici 1949
- Via an algorithm to determine the room groups . In: Comm.Math.Helvetici . 1948
- Zassenhaus and Pohst: About the calculation of class numbers and class groups of algebraic number fields . In: Journal for Pure and Applied Mathematics . 1985
- On the fundamental theorem of algebra , American Mathematical Monthly, Volume 74, 1967, p. 485 (received the Lester Randolph Ford Award )
- with Harold Brown, J. Neubüser, H. Wondratschek, R. Bülow Crystallographic groups of four dimensional space , Wiley 1978
literature
- Horst Tietz : Experienced history , communications German Mathematicians Association 1999, No. 4 (Zassenhaus in World War II)
- Wilhelm Plesken : Hans Zassenhaus (PDF; 8.8 MB) . In: Annual Report of the German Mathematicians Association , Volume 96, 1994, pp. 1-20
Web links
- Literature by and about Hans Julius Zassenhaus in the catalog of the German National Library
- Hans Julius Zassenhaus in the Mathematics Genealogy Project (English)
- Hans Zassenhaus in the Rostock matriculation portal
- John J. O'Connor, Edmund F. Robertson : Hans Julius Zassenhaus. In: MacTutor History of Mathematics archive .
- Biography at Ohio State University, English
- List of publications (Ohio State University homepage) ( Memento from September 3, 2006 in the Internet Archive )
Individual evidence
- ↑ Perhaps also because his Hamburg colleague Ernst Witt worked there, from whose National Socialist attitude he differed completely
- ^ Memories of Horst Tietz and von Zassenhaus' sister. To cover himself and others, he was officially a member of the party.
personal data | |
---|---|
SURNAME | Zassenhaus, Hans Julius |
BRIEF DESCRIPTION | German-American mathematician |
DATE OF BIRTH | May 28, 1912 |
PLACE OF BIRTH | Koblenz |
DATE OF DEATH | November 21, 1991 |
Place of death | Columbus (Ohio) , USA |