02653nam 2200457 450 991082898690332120191015173613.01-4704-5321-5(CKB)4100000009374629(MiAaPQ)EBC5904557(PPN)240204573(EXLCZ)99410000000937462920191015h20192019 uy| 0engurcnu||||||||rdacontentrdamediardacarrierMoufang loops and groups with triality are essentially the same thing /J.I. HallProvidence, RI :American Mathematical Society,[2019]©20191 online resource (206 pages) illustrationsMemoirs of the American Mathematical Society,0065-9266 ;number 1252"July 2019, volume 260, number 1252 (third of 5 numbers)."1-4704-3622-1 Includes bibliographical references and index.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."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.Memoirs of the American Mathematical Society ;no. 1252.Moufang loopsMoufang loops.512/.220-XXmscHall J. I.1653264MiAaPQMiAaPQMiAaPQBOOK9910828986903321Moufang loops and groups with triality are essentially the same thing4004461UNINA