FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2097722868> ?p ?o ?g. }

• W2097722868 abstract "The modular representation theory of Chevalley groups is still in a tentative stage (see introduction of [8]). As far as this topic is concerned, we know: indexing set for simple modules, linkage principle, strong linkage principle, blocks, etc. In this thesis two problems have been solved. Both of them deal with extension of a simple module by another simple one. The first problem deals with extension group between simple G-modules when G is universal Chevalley group, and describes this group for type A2• The second one investigates blocks of parabolic subgroups of universal Chevalley groups which is highly related to extension problem.The wide open problem of describing modular repres­entations of Chevalley groups, and solution of above mentioned problems recall to mind Hindu fable of blind men and elephant as written by J.G. Saxe, however see paragraph below.It was six men of Indostan to learning much inclined.,Who went to see Elephant (though all of them were blind)That each by observation might satisfy his mind.The First approached Elephant, and happening to fall Against his broad and sturdy side, at once began to bawl:God bless me! but Elephant is very like a wall!The Second, feeling of tusk, cried: Ho! what have we here So very round and smooth and sharp? To me ' tis very clear This wonder of an Elephant is very like a spear!The Third approached animal, ana happening to takeThe squirming trunk within his hands, thus boldly up and spake:I see, quoth he, the Elephant is very like a snake!The Fourth reached out an eager hand, and felt about knee.What most this mighty beast is like is mighty plain, quoth he;'Tis very clear Elephant is very like a tree!(The Fifth, who chawed. to touch ear, said: E'er, blindest man Can tell what this resembles rest; deny fact who can,This marvel of an Elephant is very like a fan!The Sixth no sooner had begun about beast to grope,Then, seizing on swinging tail that fell within his scope,I see, quoth he, tiie Elephant is very like a rope!And so these men of Indostan disputed loud and long,Each in his own opinion exceeding stiff and strong,Though each was partly in right, and all were in wrong!One way to study representation theory of a group is to get hold of simple modules. The modular representations of Chevalley groups (and its parabolic subgroups) are not necessarily completely reducible, so extension problem appears naturally. The natural question is, if V is a module (with two composition factors say), when is it completely reducible? Conversely, given two simple modules , L9 what modules V may be constructed with , l>2 as its composition factors, and when do these extensions split? Another important aspect of extension problem is Anderson's conjucture (conjucture 7.2 of [4]), which may be very strongly connected with Lusztig's con­juncture on character of simple modules (problem IV of [33]).This thesis consists of five chapters. Since we cannot put a sharp line between blocks and extensions, first chapter is meant to be a preliminary for both our problems, and also it presents necessary background.The second chapter deals with extension group in general (when G is universal Chevalley group), and puts some relations between extension functor and Jantzen's trans­lation functor.In third and fourth chapters we Investigate this functor when G is of type A2> In third one we determine functor Ext1U1 between simple U1--modules, where is re­stricted enveloping algebra of Lie algebra of G. The extensions Ext 1G( L (µL(λ)) i.e. between simples, have beendetermined in fourth chapter.Finally, in fifth chapter we determine blocks of parabolic subgroups of universal Chevalley groups.Throughout this thesis, notations dim and x are abbreviations for dimK and respectively xK. The symbols N, Z, Θ, IR and T will denote natural, integral, rational, real, and complex numbers respectively. Modules for affine algebraic groups will always mean rational ones defined in Section 1.1. A submodule or a direct summand may mean isomorphic to a submodule or to a direct summand. Finally, end of proofs (if any), definitions, examples, etc., will be marked thus." @default.
• W2097722868 created "2016-06-24" @default.
• W2097722868 creator A5072474171 @default.
• W2097722868 date "1982-01-01" @default.
• W2097722868 modified "2023-09-26" @default.
• W2097722868 title "Extensions of simple modules for the universal Chevalley groups and its parabolic subgroups" @default.
• W2097722868 hasPublicationYear "1982" @default.
• W2097722868 type Work @default.
• W2097722868 sameAs 2097722868 @default.
• W2097722868 citedByCount "9" @default.
• W2097722868 countsByYear W20977228682012 @default.
• W2097722868 countsByYear W20977228682014 @default.
• W2097722868 countsByYear W20977228682017 @default.
• W2097722868 crossrefType "dissertation" @default.
• W2097722868 hasAuthorship W2097722868A5072474171 @default.
• W2097722868 hasConcept C111472728 @default.
• W2097722868 hasConcept C136119220 @default.
• W2097722868 hasConcept C138885662 @default.
• W2097722868 hasConcept C202444582 @default.
• W2097722868 hasConcept C2779527642 @default.
• W2097722868 hasConcept C2780573756 @default.
• W2097722868 hasConcept C2780586882 @default.
• W2097722868 hasConcept C33923547 @default.
• W2097722868 hasConcept C41895202 @default.
• W2097722868 hasConcept C46610780 @default.
• W2097722868 hasConcept C52119013 @default.
• W2097722868 hasConcept C554144382 @default.
• W2097722868 hasConcept C95457728 @default.
• W2097722868 hasConceptScore W2097722868C111472728 @default.
• W2097722868 hasConceptScore W2097722868C136119220 @default.
• W2097722868 hasConceptScore W2097722868C138885662 @default.
• W2097722868 hasConceptScore W2097722868C202444582 @default.
• W2097722868 hasConceptScore W2097722868C2779527642 @default.
• W2097722868 hasConceptScore W2097722868C2780573756 @default.
• W2097722868 hasConceptScore W2097722868C2780586882 @default.
• W2097722868 hasConceptScore W2097722868C33923547 @default.
• W2097722868 hasConceptScore W2097722868C41895202 @default.
• W2097722868 hasConceptScore W2097722868C46610780 @default.
• W2097722868 hasConceptScore W2097722868C52119013 @default.
• W2097722868 hasConceptScore W2097722868C554144382 @default.
• W2097722868 hasConceptScore W2097722868C95457728 @default.
• W2097722868 hasLocation W20977228681 @default.
• W2097722868 hasOpenAccess W2097722868 @default.
• W2097722868 hasPrimaryLocation W20977228681 @default.
• W2097722868 hasRelatedWork W1579486099 @default.
• W2097722868 hasRelatedWork W171418171 @default.
• W2097722868 hasRelatedWork W1966760649 @default.
• W2097722868 hasRelatedWork W1969190797 @default.
• W2097722868 hasRelatedWork W1972410551 @default.
• W2097722868 hasRelatedWork W1982953013 @default.
• W2097722868 hasRelatedWork W1992941862 @default.
• W2097722868 hasRelatedWork W1999853874 @default.
• W2097722868 hasRelatedWork W2020948209 @default.
• W2097722868 hasRelatedWork W2028971234 @default.
• W2097722868 hasRelatedWork W204441696 @default.
• W2097722868 hasRelatedWork W2049202926 @default.
• W2097722868 hasRelatedWork W2074672244 @default.
• W2097722868 hasRelatedWork W2090557263 @default.
• W2097722868 hasRelatedWork W2144749697 @default.
• W2097722868 hasRelatedWork W2155619511 @default.
• W2097722868 hasRelatedWork W2490407425 @default.
• W2097722868 hasRelatedWork W2613254367 @default.
• W2097722868 hasRelatedWork W592227 @default.
• W2097722868 hasRelatedWork W7377137 @default.
• W2097722868 isParatext "false" @default.
• W2097722868 isRetracted "false" @default.
• W2097722868 magId "2097722868" @default.
• W2097722868 workType "dissertation" @default.