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Metoda Morsove teorije krajšanja v homološki algebri : doktorska disertacija
Lampret, Leon
Disertacija preučuje kvantitativne in kvalitativne lastnosti homoloških tabel standardnih objektov iz algebre in topologije. V prvem poglavju formuliramo in dokažemo Sköldbergov izrek algebraične ...Morsove teorije. V drugem si kot naše prve korake ogledamo nekaj zgledov delovanja AMT na simplicialnih kompleksih. V tretjem apliciramo AMT na bar resolventi za vnanje algebre, s tem pa dobimo novo minimalno resolvento. Z njo izračunamo Hochschildovo homologijo nad obsegi in nad ▫$\mathbb{Z}$▫, ter določimo multiplikativno strukturo kohomologije. V četrtem poglavju za družino rešljivih Liejevih algebr trikotnih matrik glede na poljubno delno urejenost konstruiramo Morsova prirejanja, ki znatno zmanjšajo verižni kompleks. V primeru linearne ureditve (torej trikotne matrike) nam ta prirejanja omogočijo temeljito preučitev tabele Chevalleyeve homologije (prosti del, prve pojavitve praštevil v torziji, nizke in visoke stopnje, homološka dimenzija). V primeru ureditev višine ▫$1$▫ in ▫$2$▫ pa nam omogočijo celo direktne izračune kohomoloških algebr.
Type of material - dissertation
; adult, serious
Publication and manufacture - Ljubljana : [L. Lampret], 2016
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