Semigroups in Algebra, Geometry and Analysis Edited by Karl H. Hofmann, Jimmie D. Lawson, and Ernest B. Vinberg de Gruyter Expositions in Mathematics, Volume 20 Berlin, 1995, xii + 370 pp., ISBN 3-11-014319-4, DM 198,-

摘要

The theory of semigroups has experienced a substantial growth in the past 10 years with applications and connections to many branches of mathematics and physics, and even to engineering problems. It shares origins with the notions of positivity and order, as well as the theory of convex cones. It also is connected to the physical concept of irreversibility, as for example encountered in diffusion processes and the heat equation. Probably best known to a mathematical audi-ence is the theory of one-parameter semigroups of operators on Banach spaces, as pioneered by Einar Hille; and it is precisely the many-parameter generalization of this, namely the theory of Lie semigroups, their geometry and their repre-sentation theory, which has proved so fruitful in the recent years. This is in no small measure due to the editors (and their students) of the present volume, which contains the contributions from participants at the Oberwolfach conference "Invariant Ordering in Geometry and Algebra" in October 1993.