Nonassociative Mathematics and its Applications
About this Title
Petr Vojtěchovský, University of Denver, Denver, CO, Murray R. Bremner, University of Saskatchewan, Saskatoon, SK, Canada, J. Scott Carter, University of South Alabama, Mobile, AL, Anthony B. Evans, Wright State University, Dayton, OH, John Huerta, University of Lisbon, Lisbon, Portugal, Michael K. Kinyon, University of Denver, Denver, CO, G. Eric Moorhouse, University of Wyoming, Laramie, WY and Jonathan D. H. Smith, Iowa State University, Ames, IA, Editors
Publication: Contemporary Mathematics
Publication Year: 2019; Volume 721
ISBNs: 978-1-4704-4245-3 (print); 978-1-4704-5102-8 (online)
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.
Graduate students and research mathematicians interested in nonassociative algebraic structures, Lie algebras, and Jordan algebras.
Table of Contents
- A. Anastasiou, L. Borsten, M. J. Duff, A. Marrani, S. Nagy and M. Zoccali – The mile high magic pyramid$^*$
- Murray R. Bremner – Symmetrization of Jordan dialgebras
- J. Scott Carter, Victoria Lebed and Seung Yeop Yang – A prismatic classifying space
- Patrick Dehornoy – Some aspects of the SD-world
- Aleš Drápal – About Laver tables
- Jörg Feldvoss – Leibniz algebras as non-associative algebras
- Mark Greer – Simple right conjugacy closed loops
- Bokhee Im and Jonathan D. H. Smith – Orthogonality of approximate Latin squares and quasigroups
- Sujoy Mukherjee and Józef H. Przytycki – On the rack homology of graphic quandles
- Alex Nowak – Modules over semisymmetric quasigroups
- J. D. Phillips – Moufang and commutant elements in magmas
- S. Pumplün – The multiplicative loops of Jha-Johnson semifields
- Anna Romanowska – Convex sets and barycentric algebras
- Izabella Stuhl and Petr Vojtěchovský – Enumeration of involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order
- Piero Truini, Michael Rios and Alessio Marrani – The magic star of exceptional periodicity