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E-raamat: Moufang Loops and Groups with Triality are Essentially the Same Thing

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In 1978, Stephen Doro showed that Moufang loops and groups with triality are essentially the same thing-"essentially" because the most obvious categories of them are not in fact equivalent. In sections on basics, equivalence, related topics, and classical triality, Hill makes Doro's statement precise in a categorical context. Among the topics are Latin square designs, Moufang loops and groups with triality are essentially (but not exactly) the same thing, some related categories and objects, orthogonal spaces and groups, and the loop of units in an octonian algebra. Annotation ©2019 Ringgold, Inc., Portland, OR (protoview.com)
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.
J. I. Hall, Michigan State University, East Lansing.