Ring theorists and researchers in invariant theory and operator algebra met at Bowdoin for the 1984 AMS-IMS-SIAM Joint Summer Research Conference to exchange ideas about group actions on rings and to stimulate general interaction among their various fields. Collecting together the proceedings of that meeting, this interdisciplinary volume reveals many topics common to the three fields: \(K\)-theory, dual actions, semi-invariants, and crossed products. A high percentage of the papers here are expository; of particular significance are the papers by the four survey lecturers, Edward Formanek on noncommutative invariant theory; Melvin Hochster on invariant theory of commutative rings; D. S. Passman on algebraic crossed products; and Marc A. Reiffel on \(K\)-theory of crossed products of \(C*\)-algebras by discrete groups.

Table of Contents

• H. Bass -- Algebraic group actions on affine spaces
• G. M. Bergman -- Everybody knows what a Hopf algebra is
• M. Cohen -- Hopf algebras acting on semiprime algebras
• W. Dicks -- Automorphisms of the free algebra of rank two
• D. R. Farkas -- Toward multiplicative invariant theory
• J. W. Fisher -- Invariants of finite linear groups acting on relatively free algebras: a survey
• E. Formanek -- Noncommutative invariant theory
• R. M. Fossum -- Invariants and formal group law actions
• D. Handelman -- Classification of compact group actions on locally semisimple algebras
• R. H. Herman -- The Rohlin property for automorphism of UHF \(C^*\)-algebras
• M. Hochster -- Invariant theory of commutative rings
• V. F. R. Jones -- Index for subrings of rings
• S. Montgomery -- Duality for actions and coactions of groups
• D. S. Passman -- Algebraic crossed products
• N. C. Phillips -- \(K\)-theoretic freeness of finite group actions on \(C^*\)-algebras
• I. Reiten -- Skew group rings in the computation of Grothendieck groups and in the representation theory of Artin algebras
• M. A. Reiffel -- \(K\)-theory of crossed products of \(C^*\)-algebras by discrete groups
• D. J. Saltman -- Groups acting on fields: Noether's problem