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Nonassociative mathematics and its applications : fourth Mile High Conference on Nonassociative Mathematics, July 29-August 5, 2017, University of Denver, Denver, Colorado
- Author / Creator
- Conferences
- Mile High Conference on Nonassociative Mathematics (4th : 2017 : Denver, Colo.)
- Available as
- Online
- Summary
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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 quasigro...
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.
Details
- Creator
- Petr Vojtěchovský [and seven others], editors
- Format
- Books
- Language
- English
- Publication
-
- 1st ed
- Providence, RI : American Mathematical Society, [2019]
- ©2019
- Physical Details
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- 1 online resource (310 pages)
- ISBNs
- 1470451026, 9781470451028, 9781470442453, 1470442450
- OCLC
- on1086066733, on1082870433
- Includes bibliographical references.
- English
- Cover -- Title page -- Contents -- Introduction -- The mile high magic pyramid* -- 1. Introduction -- 2. Physics background -- 3. The normed division algebras -- 4. The magic pyramid of supergravities -- 5. Conclusion -- Acknowledgment -- References -- Symmetrization of Jordan dialgebras -- 1. Introduction -- 2. Algebraic operads -- 3. Degrees 4 and 5 -- 4. Degree 6 -- 5. Degree 7 -- Acknowledgments -- References -- A prismatic classifying space -- 1. Introduction -- 2. Prismatic homology -- 3. Simplicial and cubical classifying spaces -- 4. Prismatic classifying spaces -- 5. Knottings of dimension 1 and 2 -- 6. Prismatic homology with degeneracies -- 7. Homological invariants of knottings -- Acknowledgments -- References -- Some aspects of the SD-world -- 1. Shelves, spindles, racks, and quandles -- 2. Word problem, the case of shelves I -- 3. Word problem, the case of shelves II -- 4. Word problem, the case of racks, quandles, and spindles -- References -- About Laver tables -- 1. Operations -- 2. Elements and periods -- 3. Homomorphisms -- Acknowledgments and final comments -- References -- Leibniz algebras as non-associative algebras -- Introduction -- 1. Non-associative algebras -- 2. Leibniz algebras -definition and examples -- 3. Leibniz modules -- 4. Leibniz cohomology -- 5. Nilpotent Leibniz algebras -- 6. Solvable Leibniz algebras -- 7. Semisimple Leibniz algebras -- Acknowledgments -- References -- Simple right conjugacy closed loops -- 1. Introduction -- 2. Right conjugacy closed loops -- 3. Constructing simple RCC loops -- 4. Isomorphism classes -- Acknowledgments -- References -- Orthogonality of approximate Latin squares and quasigroups -- 1. Introduction -- 2. Approximate quasigroups and Latin squares -- 3. Orthogonality of approximate Latin squares -- 4. Fields, quasigroups, and Latin squares -- 5. Extension of orthogonality
- 6. The projective geometry of orthogonality -- 7. The discrete distance -- Acknowledgment -- References -- On the rack homology of graphic quandles -- 1. Introduction -- 2. Rack and quandle homology -- 3. Odds and ends -- Acknowledgments -- References -- Modules over semisymmetric quasigroups -- 1. Introduction -- 2. Semisymmetric quasigroups -- 3. Multiplication groups -- 4. Quasigroup modules -- Acknowledgment -- References -- Moufang and commutant elements in magmas -- 1. Introduction and a note on Prover9 -- 2. Moufang elements and two new submagmas -- 3. The left semimedial law -- 4. The middle semimedial law and a new submagma -- 5. A general setting for Moufang theorems -- 6. Acknowledgment -- References -- The multiplicative loops of Jha-Johnson semifields -- Introduction -- 1. Preliminaries -- 2. The automorphisms of the multiplicative loops of _{ } -- 3. Inner automorphisms -- 4. Nonassociative cyclic algebras -- 5. Isotopies -- References -- Convex sets and barycentric algebras -- 1. Introduction -- 2. Affine spaces and convex sets -- 3. The structure of barycentric algebras -- 4. Barycentric algebras as entropic algebras -- 5. Extended barycentric algebras -- 6. Duality -- 7. Threshold barycentric algebras -- References -- Enumeration of involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order -- 1. Introduction -- 2. Notation and background material -- 3. Two correspondences -- 4. Central extensions of loops -- 5. Central extensions of left Bruck loops and commutative automorphic loops -- 6. The algorithm -- 7. Results -- 8. Open problems -- Acknowledgments -- References -- The magic star of exceptional periodicity -- 1. Introduction -- 2. Jordan structures and related Lie algebras -- 3. The magic star: Exceptional Lie algebras and Jordan structures
- 4. Exceptional periodicity and extended roots -- 5. The \lms algebra -- 6. T-algebras -- 7. Future developments -- References -- Back Cover