Moufang Loops and Groups with Triality Are Essentially the Same Thing
American Mathematical Society (Verlag)
978-1-4704-3622-3 (ISBN)
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In 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.''
J. I. Hall, Michigan State University, East Lansing.
Part 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.
| Erscheinungsdatum | 02.09.2019 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 297 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-3622-1 / 1470436221 |
| ISBN-13 | 978-1-4704-3622-3 / 9781470436223 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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