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 ( BA 1944) and Cornell University, with a master's degree in 1945 ( with a theme from number theory of binary quadratic forms) and the PhD in 1949 at Burton Jones (A generalization of Meyer 's theorem ). He was from the early 1950s, a professor at the University of Illinois at Urbana- Champaign.

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

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

In 1962 he was Guggenheim Fellow and 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).

Writings

  • With Charles W. Curtis Representation theory of finite groups and associated algebras, Wiley 1962, new edition 1981/82 in two sets as Methods of representation theory: with applications to finite groups and orders, Wiley
  • Representations of cyclic groups in rings of integers, 1,2, Annals of Mathematics, Volume 76, 1962, pp. 73-92, Vol 77, 1963, pp. 318-328
  • Maximum Orders, Academic Press, 1975, Oxford University Press 2003
  • Class groups and Picard groups of group rings and orders, American Mathematical Society 1976
  • Integral representation algebras, Transactions AMS, 124, 1966, 111-121
  • Klaus W. Roggenkamp integral representations, Lecture Notes in Mathematics, Springer Verlag 1979
  • With Tsit Yuen Lam Relative Grothendieck Groups, J. Algebra, 11, 1969, 213-242
  • With LK Hua automorphisms of the unimodular group, Transactions AMS, 71, 1951, 331-348
  • Integral representations of cyclic groups of prime order, Proc. AMS, 8, 1957, 142-146
  • With A. Heller Grothendieck groups of orders in semisimple algebras, Transactions AMS, 112, 1964, 344-355
  • S. Ullom class groups of integral group rings, Transactions AMS, 170, 1972, 1-30
  • A survey of integral representation theory, Bulletin AMS, 76, 1970, 159-227, online
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