349 KB27 KB200820252016Franchi, ClaraIvanov, Alexander A.Mainardis, Marioštevilka:1letnik:11str. 175-187COBISSID:17845849ISSN:1855-3966URN:URN:NBN:SI:doc-2J3ZJXJSenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneaalgebra Pošastasociativne shemeassociation schemesHarada-Norton groupHarada-Nortonova grupaMajorana representationsMajoranova reprezentacijamonster algebraThe 2A-Majorana representations of the Harada-Norton group|We show that all 2?$A$?-Majorana representations of the Harada-Norton group ?$F_{5}$? have the same shape. If ?$\mathcal{R}$? is such a representation, we determine, using the theory of association schemes, the dimension and the irreducible constituents of the linear span ?$U$? of the Majorana axes. Finally, we prove that, if ?$\mathcal{R}$? is based on the (unique) embedding of ?$F_{5}$? in the Monster, ?$U$? is closed under the algebra productPokažemo, da imajo vse 2?$A$?-Majoranove reprezentacije Harada-Nortonove grupe ?$F_{5}$? enako obliko. Vsaki takšni reprezentaciji ?$\mathcal{R}$? s pomočjo teorije asociativnih shem določimo dimenzijo in ireducibilne sestavine linearne lupine ?$U$? njenih Majoranovih osi. Nazadnje dokažemo: če ?$\mathcal{R}$? bazira na (enolični) vložitvi ?$F_{5}$? v algebro Pošast, potem je ?$U$? zaprta glede na algebrski produktTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije