Integral Representations and Applications Proceedings of a Conferenc
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882 Integral Representations and Applications Proceedings of a Conference held at Oberwolfach, Germany, June 22-28, 1980
Edited by Klaus W. Roggenkamp
Springer-Verlag Berlin Heidelberg New York 1981
Editor
Klaus W. Roggenkamp Mathematisches Institut B, Universitat Stuttgart Pfaffenwaldring 57, 7000 Stuttgart 80, Federal Republic of Germany
AMS Subject Classifications (1980): 12A57, 12A62, 15A36, 16A 18, 20ClO ISBN 3-540-10880-7 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-10880-7 Springer-Verlag New York Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1981 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
INTRODUCTION
Integral representation theory and applications thereof
have over
the past years made considerable progress. The intention of the Oberwolfach meeting in 1980 was to demonstrate the various applications of orders to number theory, topology, geometry and
crystallography and also to show the influences these vari-
ous subjects have had on integral representation theory.
Apart from
these} new trends in integral representation theory were presented: Almost split sequences and AuslanderReiten graphs in connection with classification of indecomposable lattices} and
on lattices.
ThuS we had several survey talks: "Orders in geometry, topology and number theory"; "Algebraic aspects of crystallography"; "Graham Higman's thesis" (it was surprising to hear of the wealth of results in Higman's 1940 thesis which escaped the attention of people working on the subject Higman's thesis never being published and thus were reproved between 1960 and 1980); "Zetafunctions of orders"; "The class group
a la
Frohlich"
"Integral representations in the study of finite Poincare complexes" ; "Poset representations" (unfortunately Ludmilla Nazarova was the only one of the soviet mathematicians working in representation theory who was able to attend the meeting) ; "Preprojective lattices over orders over Dedekind domains"; "Projective modules and resolutions for finite groups".
IV
After some hesitation - being aware of the complications - the contributions in these notes appear not alphabetically but according subjects. Part I contains the historical aspects leading to crystallography and via units to finite conjugate subrings of orders and via personal connections to constructive methods in ideal theory. Part II deals with '-functions of orders - influenced by number theory - and Galois module structure - as applications of integral representations to number theory - in its various aspects. Part III gives applicatio
