Moufang loops and groups with triality are essentially the same thing / J.I. Hall.
| Author/creator | Hall, J. I. |
| Format | Electronic |
| Publication Info | Providence, RI : American Mathematical Society, [2019] |
| Description | xiv, 186 pages : illustrations ; 26 cm |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Subjects |
| Series | Memoirs of the American Mathematical Society, 0065-9266 ; number 1252 |
| Contents | Category theory -- Quasigroups and loops -- Latin square designs -- Groups with triality -- The functor B -- Monics, covers, and isogeny in 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 -- The functors S and M -- The functor G -- Multiplication groups and autotopisms -- Doro's approach -- Normal structure -- Some related categories and objects -- 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. |
| Abstract | "In 1925, Elie Cartan introduced the principal of triality specifically for the Lie groups of type D4, and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title was made by Stephen Doro in 1978 who was in turn motivated by work of George Glauberman from 1968. Here we make 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.""-- Provided by publisher. |
| Bibliography note | Includes bibliographical references. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2020058311 |
| ISBN | 9781470436223 (paperback) |
| ISBN | (pdf) |