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Author: Patrick Dehornoy
Publisher: Birkhäuser
ISBN: 3034884427
Category : Mathematics
Languages : en
Pages : 637
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Book Description
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.
Author: Patrick Dehornoy
Publisher: Birkhäuser
ISBN: 3034884427
Category : Mathematics
Languages : en
Pages : 637
Get Book
Book Description
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.
Author: Patrick Dehornoy
Publisher: American Mathematical Soc.
ISBN: 0821844318
Category : Braid theory
Languages : en
Pages : 339
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Book Description
Since the discovery that Artin's braid groups enjoy a left-invariant linear ordering, several different approaches have been used to understand this phenomenon. This text provides an account of those approaches, involving varied objects & domains as combinatorial group theory, self-distributive algebra & finite combinatorics.
Author: Martin Kreuzer
Publisher: American Mathematical Soc.
ISBN: 0821840371
Category : Algebra
Languages : en
Pages : 190
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Book Description
The book consists of contributions related mostly to public-key cryptography, including the design of new cryptographic primitives as well as cryptanalysis of previously suggested schemes. Most papers are original research papers in the area that can be loosely defined as ``non-commutative cryptography''; this means that groups (or other algebraic structures) which are used as platforms are non-commutative.
Author: Petr Vojtěchovský
Publisher: American Mathematical Soc.
ISBN: 1470442450
Category : Nonassociative algebras
Languages : en
Pages : 297
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Book Description
Nonassociative mathematics is a broad research area that studies mathematical structures violating the associative law x(yz)=(xy)z. The topics covered by nonassociative mathematics include quasigroups, loops, Latin squares, Lie algebras, Jordan algebras, octonions, racks, quandles, and their applications. This volume contains the proceedings of the Fourth Mile High Conference on Nonassociative Mathematics, held from July 29–August 5, 2017, at the University of Denver, Denver, Colorado. Included are research papers covering active areas of investigation, survey papers covering Leibniz algebras, self-distributive structures, and rack homology, and a sampling of applications ranging from Yang-Mills theory to the Yang-Baxter equation and Laver tables. An important aspect of nonassociative mathematics is the wide range of methods employed, from purely algebraic to geometric, topological, and computational, including automated deduction, all of which play an important role in this book.
Author: K. Glazek
Publisher: Springer Science & Business Media
ISBN: 9401599645
Category : Mathematics
Languages : en
Pages : 394
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Book Description
This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).
Author: Christian Kassel
Publisher: Springer Science & Business Media
ISBN: 0387685480
Category : Mathematics
Languages : en
Pages : 349
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Book Description
In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices. Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 400
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Book Description
Author: Vassily Olegovich Manturov
Publisher: CRC Press
ISBN: 1351359126
Category : Mathematics
Languages : en
Pages : 528
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Book Description
Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text. Knot Theory, Second Edition is notable not only for its expert presentation of knot theory’s state of the art but also for its accessibility. It is valuable as a profes-sional reference and will serve equally well as a text for a course on knot theory.
Author: Patrick Dehornoy
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 220
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Book Description
In the decade since the discovery that Artin's braid groups enjoy a left-invariant linear ordering, several quite different approaches have been applied to understand this phenomenon. This book is an account of those approaches, involving self-distributive algebra, uniform finite trees, combinatorial group theory, mapping class groups, laminations, and hyperbolic geometry. This volume is suitable for graduate students and research mathematicians interested in algebra and topology.
Author: Matthew Foreman
Publisher: Springer Science & Business Media
ISBN: 1402057644
Category : Mathematics
Languages : en
Pages : 2230
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Book Description
Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.
