Irving Reiner

Irving Reiner (born February 8, 1924 in Brooklyn , † October 28, 1986 in Urbana (Illinois) ) was an American mathematician who dealt with representation theory of algebras and groups and number theory.

Reiner studied at Brooklyn College (bachelor's degree in 1944) and at Cornell University , with a master's degree in 1945 (with a topic from number theory of binary quadratic forms) and his doctorate in 1949 with Burton Jones ( A generalization of Meyer´s theorem ) . He was a professor at the University of Illinois at Urbana-Champaign from the early 1950s .

From 1947/48 and 1954 to 1956 he was at the Institute for Advanced Study . He was visiting professor in London and at the University of Warwick, among others.

Initially he dealt with questions about the general linear group over the whole numbers (automorphisms, classical subgroups, generators, etc.), from around 1955 with representation theory. His book with Charles W. Curtis (then at the University of Wisconsin at Madison) on representation theory of finite groups and associated algebras is a standard work and made both known.

In 1962 he was a Guggenheim Fellow and in 1963 he received a Distinguished Alumni Award from Brooklyn College.

With Klaus Roggenkamp he organized several Oberwolfach conferences (such as Orders and their Applications 1984).

Fonts

• with LK Hua : Automorphisms of the unimodular group. In: Transactions of the American Mathematical Society . Volume 71, No. 3, 1951, pp. 331-348, doi : 10.2307 / 1990696 .
• Integral representations of cyclic groups of prime order. In: Proceedings of the American Mathematical Society . Volume 8, No. 1, 1957, 142-146, doi : 10.2307 / 1990696 .
• with Charles W. Curtis: Representation theory of finite groups and associative algebras (= Pure and Applied Mathematics. 11). Interscience Publishers, New York NY et al. 1962, (New edition in two volumes as: Methods of representation theory. With applications to finite groups and orders. Wiley, New York NY et al. 1981–1987, ISBN 0-471-18994-4 (Vol. 1), ISBN 0-471-88871-0 (Vol. 2)).
• with Alex Heller : Representations of cyclic groups in rings of integers. 1, 2. In: Annals of Mathematics . Series 2, Vol. 76, No. 1, 1962, pp. 73-92, doi : 10.2307 / 1970266 ; Volume 77, No. 2, 1963, pp. 318-328, doi : 10.2307 / 1970218 .
• with Alex Heller: Grothendieck Groups of Orders in semisimple algebras. In: Transactions of the American Mathematical Society. Volume 112, No. 2, 1964, pp. 344-355, doi : 10.2307 / 1994300 .
• Integral representation algebras. In: Transactions of the American Mathematical Society. Vol. 124, No. 1, 1966, pp. 111-121, doi : 10.2307 / 1994438 .
• with Tsit Yuen Lam : Relative Grothendieck Groups. In: Journal of Algebra. Volume 11, No. 2, 1969, pp. 213-242, doi : 10.1016 / 0021-8693 (69) 90055-6 .
• A survey of integral representation theory. In: Bulletin of the American Mathematical Society . Volume 76, No. 2, 1970, pp. 159-227, doi : 10.1090 / S0002-9904-1970-12441-7 .
• with Stephen Ullom: Class groups of integral group rings. In: Transactions of the American Mathematical Society. Volume 170, 1972, pp. 1-30, doi : 10.2307 / 1996291 .
• Maximum orders (= LMS Monographs. 5). Academic Press, London et al. 1975, ISBN 0-12-586650-X (Reissued with corrections and new foreword. (= London Mathematical Society Monographs. New Series. 28). Oxford University Press, Oxford et al. 2003, ISBN 0-19-852673 -3 .
• Class groups and Picard groups of group rings and orders (= Regional Conference Series in Mathematics. 26). American Mathematical Society, Providence RI 1976, ISBN 0-8218-1676-4 .
• Topics in integral representation theory. In: Reiner, Klaus W. Roggenkamp : Integral representations (= Lecture Notes in Mathematics . 744). Springer, Berlin et al. 1979, ISBN 3-540-09546-2 , pp. 1-143.

Web links

• John J. O'Connor, Edmund F. Robertson :  Irving Reiner. In: MacTutor History of Mathematics archive .

Individual evidence

1. ↑ Irving Reiner in the Mathematics Genealogy Project (English)