Free Delivery Over $100
|
|
|||
|
||||
OverviewIn 1925 Elie Cartan introduced the principal of triality specifically for the Lie groups of type $D_4$, and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title in 1978 was made by Stephen Doro, who was in turn motivated by the work of George Glauberman from 1968. Here the author makes the statement precise in a categorical context. In fact the most obvious categories of Moufang loops and groups with triality are not equivalent, hence the need for the word ``essentially.'' Full Product DetailsAuthor: J.I. HallPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.297kg ISBN: 9781470436223ISBN 10: 1470436221 Pages: 188 Publication Date: 30 October 2019 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPart 1. Basics: Category theory Quasigroups and loops Latin square designs Groups with triality Part 2. Equivalence: The functor ${\mathbf {B}}$ Monics, covers, and isogeny in $\mathsf {TriGrp}$ Universals and adjoints Moufang loops and groups with triality are essentially the same thing Moufang loops and groups with triality are not exactly the same thing Part 3. Related Topics: The functors ${\mathbf {S}}$ and ${\mathbf {M}}$ The functor ${\mathbf {G}}$ Multiplication groups and autotopisms Doro's approach Normal Structure Some related categories and objects Part 4. Classical Triality: An introduction to concrete triality Orthogonal spaces and groups Study's and Cartan's triality Composition algebras Freudenthal's triality The loop of units in an octonion algebra Bibliography Index.ReviewsAuthor InformationJ. I. Hall, Michigan State University, East Lansing. Tab Content 6Author Website:Countries AvailableAll regions |
||||
