Theory of K-loops
Author(s)
Bibliographic Information
Theory of K-loops
（Lecture notes in mathematics, 1778）
Springer, c2002
Available at / 72 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||177878800462
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INTERNATIONAL CHRISTIAN UNIVERSITY LIBRARY図
V.1778410.8/L507/v.177805768822,
410.8/L507/v.177805768822 -
Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC21:512.2/K5412070559006
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Note
Includes bibliographical references (p. [171]-180) and index
Description and Table of Contents
Description
The book contains the first systematic exposition of the current known theory of K-loops, as well as some new material. In particular, big classes of examples are constructed. The theory for sharply 2-transitive groups is generalized to the theory of Frobenius groups with many involutions. A detailed discussion of the relativistic velocity addition based on the author's construction of K-loops from classical groups is also included. The first chapters of the book can be used as a text, the later chapters are research notes, and only partially suitable for the classroom. The style is concise, but complete proofs are given. The prerequisites are a basic knowledge of algebra such as groups, fields, and vector spaces with forms.
Table of Contents
Introduction.- Preliminaries.- Left Loops and Transversals.- The Left Inverse Property and Kikkawa Loops.- Isotopy Theory.- Nuclei and the Autotopism Group.- Bol Loops and K-Loops.- Frobenius Ggroups with Mmany Involutions.- Loops with Fibrations.- K-Loops from Classical Groups over Ordered Fields.- Relativistic Velocity Addition.- K-Loops from the General Linear Groups over Rings.- Derivations.
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