LEADER 02653nam 2200457 450 001 9910828986903321 005 20191015173613.0 010 $a1-4704-5321-5 035 $a(CKB)4100000009374629 035 $a(MiAaPQ)EBC5904557 035 $a(PPN)240204573 035 $a(EXLCZ)994100000009374629 100 $a20191015h20192019 uy| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aMoufang loops and groups with triality are essentially the same thing /$fJ.I. Hall 210 1$aProvidence, RI :$cAmerican Mathematical Society,$d[2019] 210 4$dİ2019 215 $a1 online resource (206 pages) $cillustrations 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 1252 300 $a"July 2019, volume 260, number 1252 (third of 5 numbers)." 311 $a1-4704-3622-1 320 $aIncludes bibliographical references and index. 327 $aCategory 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. 330 $a"In 1925, Elie Cartan introduced the principal of triality specifically for the Lie groups of type D4, and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title was made by Stephen Doro in 1978 who was in turn motivated by work of George Glauberman from 1968. Here we make the statement precise in a categorical context. In fact the most obvious categories of Moufang loops and groups with triality are not equivalent, hence the need for the word "essentially.""--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society ;$vno. 1252. 606 $aMoufang loops 615 0$aMoufang loops. 676 $a512/.2 686 $a20-XX$2msc 700 $aHall$b J. I.$01653264 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910828986903321 996 $aMoufang loops and groups with triality are essentially the same thing$94004461 997 $aUNINA