Nonassociative Mathematics and Its Applications
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 applica...
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| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Providence :
American Mathematical Society,
2019
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| Series: | Contemporary Mathematics Ser.
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| Subjects: | |
| Local Note: | ProQuest Ebook Central |
Table of Contents:
- 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 degeneracies7. 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 modules4. 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 orthogonality7. 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 theorems6. 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
