"Oktonion"@cs . . "V matematice se pojmem oktoniony ozna\u010Duje neasociativn\u00ED roz\u0161\u00ED\u0159en\u00ED kvaternion\u016F. Tvo\u0159\u00ED osmidimenzion\u00E1ln\u00ED algebru nad re\u00E1ln\u00FDmi \u010D\u00EDsly, nejstar\u0161\u00ED zn\u00E1m\u00FD p\u0159\u00EDklad neasociativn\u00EDho okruhu.Oktoniony tvo\u0159\u00ED posledn\u00ED, a tud\u00ED\u017E nejobecn\u011Bj\u0161\u00ED typ tzv. normovan\u00FDch algeber s d\u011Blen\u00EDm (t\u00E9\u017E naz\u00FDvan\u00E9 Hurwitzovy algebry). Je velmi p\u0159ekvapiv\u00E9, \u017Ee existuj\u00ED pr\u00E1v\u011B jen \u010Dty\u0159i takov\u00E9 algebry: Re\u00E1ln\u00E1 \u010D\u00EDsla, komplexn\u00ED \u010D\u00EDsla, kvaterniony a oktoniony. Principi\u00E1ln\u00ED rozd\u00EDl mezi vektorov\u00FDmi prostory a Hurwitzov\u00FDmi algebrami spo\u010D\u00EDv\u00E1 pr\u00E1v\u011B v operaci d\u011Blen\u00ED: zat\u00EDmco u vektor\u016F operaci d\u011Blen\u00ED dvou vektor\u016F v\u016Fbec nezav\u00E1d\u00EDme (neexistuje), u normovan\u00FDch algeber s d\u011Blen\u00EDm (vz\u00E1jemn\u011B jednozna\u010Dn\u00E1 a invertibiln\u00ED) operace d\u011Blen\u00ED existuje. Hurwitzovy algebry v\u0161ak existuj\u00ED jen ve \u010Dty\u0159ech v\u00FDlu\u010Dn\u00FDch dimenz\u00EDch: 1, 2, 4, 8. Dimenze 8 m\u00E1 tedy ur\u010Dit\u00E9 unik\u00E1tn\u00ED vlastnosti, dan\u00E9 unik\u00E1tn\u00EDmi vlastnostmi oktonion\u016F. Zat\u00EDmco re\u00E1ln\u00E1 \u010D\u00EDsla, komplexn\u00ED \u010D\u00EDsla a kvaterniony maj\u00ED t\u011Bsn\u00FD vztah k regul\u00E1rn\u00EDm Lieov\u00FDm grup\u00E1m typu A, B, C, D, oktoniony maj\u00ED t\u011Bsn\u00FD vztah k tzv. v\u00FDlu\u010Dn\u00FDm Lieov\u00FDm grup\u00E1m typu G2, F4, E6, E7, E8. \u0158ada teoretick\u00FDch fyzik\u016F proto opr\u00E1vn\u011Bn\u011B usuzuje t\u00E9\u017E na hlubokou roli oktonion\u016F ve fyzice, zejm\u00E9na \u010D\u00E1sticov\u00E9.Z\u0159ejm\u011B kv\u016Fli neasociativnosti, kter\u00E1 je zd\u00E1nliv\u011B \u201Enefyzik\u00E1ln\u00ED\u201C, jsou oktoniony dosud m\u00E9n\u011B zn\u00E1m\u00E9 i pou\u017E\u00EDvan\u00E9 ne\u017E kvaterniony.M\u00EDrou naru\u0161en\u00ED komutativn\u00EDho a asociativn\u00EDho z\u00E1kona jsou u oktonion\u016F veli\u010Diny zvan\u00E9 komut\u00E1tor a asoci\u00E1tor."@cs . "26423"^^ . . . . . . . . "Oktonion"@cs . . . "V matematice se pojmem oktoniony ozna\u010Duje neasociativn\u00ED roz\u0161\u00ED\u0159en\u00ED kvaternion\u016F. Tvo\u0159\u00ED osmidimenzion\u00E1ln\u00ED algebru nad re\u00E1ln\u00FDmi \u010D\u00EDsly, nejstar\u0161\u00ED zn\u00E1m\u00FD p\u0159\u00EDklad neasociativn\u00EDho okruhu.Oktoniony tvo\u0159\u00ED posledn\u00ED, a tud\u00ED\u017E nejobecn\u011Bj\u0161\u00ED typ tzv. normovan\u00FDch algeber s d\u011Blen\u00EDm (t\u00E9\u017E naz\u00FDvan\u00E9 Hurwitzovy algebry). Je velmi p\u0159ekvapiv\u00E9, \u017Ee existuj\u00ED pr\u00E1v\u011B jen \u010Dty\u0159i takov\u00E9 algebry: Re\u00E1ln\u00E1 \u010D\u00EDsla, komplexn\u00ED \u010D\u00EDsla, kvaterniony a oktoniony."@cs . . . . . "3763"^^ . "16282800"^^ . . . . . "27"^^ . . . . . . "Cayleyovo \u010D\u00EDslo"@cs . . "oktonion"@cs . . . . . .