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Full 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.
Contents
A. Anastasiou, L. Borsten, M. J. Duff, A. Marrani, S. Nagy, and M. Zoccali, The mile high magic pyramid
M. R. Bremner, Symmetrization of Jordan dialgebras
J. S. Carter, V. Lebed, and S. Y. Yang, A prismatic classifying space
P. Dehornoy, Some aspects of the SD-world
A. Drapal, About Laver tables
J. Feldvoss, Leibniz algebras as non-associative algebras
M. Greer, Simple right conjugacy closed loops
B. Im and J. D. H. Smith, Orthogonality of approximate Latin squares and quasigroups
S. Mukherjee and J. H. Przytycki, On the rack homology of graphic quandles
A. Nowak, Modules over semisymmetric quasigroups
J. D. Phillips, Moufang and commutant elements in magmas
S. Pumplun, The multiplicative loops of Jha-Johnson semifields
A. Romanowska, Convex sets and barycentric algebras
I. Stuhl and P. Vojtechovsky, Enumeration of involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order
P. Truini, M. Rios, and A. Marrani, The magic star of exceptional periodicity.
