Handbook of Algebra, Volume 4

Preface Outline of the Series List of Contributors Section 2C. Algebraic K-theory Higher Algebraic K-theory (A. Kuku) Section 3B. Associative Rings and Algebras Filter Dimension (V.V. Bavula) Section 4E. Lie Algebras Gelfand-Tsetlin Bases for Classical Lie Algebras (A.I. Molev) Section 4H. Rings and Algebras with Additional Structure Hopf Algebras (M. Cohen, S. Gelaki and S. Westreich) Difference Algebra (A.B. Levin) Section 5A. Groups and Semigroups Reflection Groups (M. Geck and G. Malle) Hurwitz Groups and Hurwitz Generation (M.C. Tamburini and M. Vsemirnov) Survey on Braids (V. Vershinin) Groups with Finiteness Conditions (V.I. Senashov) Index

Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest.

In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc.

The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published.

A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed.

• Thorough and practical source for information
• Provides in-depth coverage of new topics in algebra
• Includes references to relevant articles, books and lecture notes

Researchers, students, and professionals working in both pure and applied mathematics.