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ISBN-13:
9783034884426
Veröffentl:
2012
Seiten:
623
Autor:
Patrick Dehornoy
Serie:
192, Progress in Mathematics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
This is the award-winning monograph of the Sunyer i Balaguer Prize 1999. The book presents recently discovered connections between Artin's braid groups and left self-distributive systems, which are sets equipped with a binary operation satisfying the identity x(yz) = (xy)(xz). Although not a comprehensive course, the exposition is self-contained, and many basic results are established. In particular, the first chapters include a thorough algebraic study of Artin's braid groups.
A: Ordering the Braids.- I. Braids vs. Self-Distributive Systems.- II. Word Reversing.- III. The Braid Order.- IV. The Order on Positive Braids.- B: Free LD-systems.- V. Orders on Free LD-systems.- VI. Normal Forms.- VII. The Geometry Monoid.- VIII. The Group of Left Self-Distributivity.- IX. Progressive Expansions.- C: Other LD-Systems.- X. More LD-Systems.- XI. LD-Monoids.- XII. Elementary Embeddings.- XIII. More about the Laver Tables.- List of Symbols.