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On pairs of commuting nilpotent matricesKošir, Tomaž, 1962- ; Oblak, Polona, matematikaNaj bo ▫$B$▫ nilpotentna matrika, katere Jordanova kanonična forma je podana s particijo ▫$\lambda$▫. Znano je, da je njen nilpotentni komutator ▫${\mathcal{N}}_B$▫ nerazcepna raznoterost in da ... obstaja natanko ena particija ▫$\mu$▫, za katero je presek nilpotentne orbite, ki pripada ▫$\mu$▫, in nilpotentnega komutatorja ▫${\mathcal{N}}_B$▫ gosta množica v ▫${\mathcal{N}}_B$▫. Pokažemo, da je preslikava ▫$\mathcal{D}$▫, podana s predpisom ▫${\mathcal{D}}(\lambda) = \mu$▫, idempotentna. S tem odgovorimo na vprašanje, ki sta ga zastavila Basilijeva in Iarrobino in delno odgovorimo tudi na Panyushevo vprašanje. V dokazu bomo uporabili dejstvo, da je za generično matriko ▫$A \in {\mathcal{N}}_B$▫ algebra, generirana z matrikama ▫$A$▫ in ▫$B$▫, Gorensteinova. Zato generični par komutirajočih nilpotentnih matrik generira Gorensteinovo algebro. Opišemo tudi ▫${\mathcal{D}}(\lambda)$▫ v odvisnosti od particije ▫$\lambda$▫ v primeru, ko ima particija ▫${\mathcal{D}}(\lambda)$▫ kvečjemu dva dela.Source: Transformation groups. - ISSN 1083-4362 (Vol. 14, no. 1, 2009, str. 175-182)Type of material - article, component partPublish date - 2009Language - englishCOBISS.SI-ID - 15077977
Author
Košir, Tomaž, 1962- |
Oblak, Polona, matematika
Topics
matematika |
linearna algebra |
komutirajoče matrike |
nilpotentne matrike |
nilpotentni komutator |
nilpotentna orbita |
Gorensteinova algebra |
mathematics |
linear algebra |
commuting matrices |
nilpotent matrices |
nilpotent commutator |
nilpotent orbit |
maximal partition |
Gorenstein artinian algebra
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Košir, Tomaž, 1962- | 08398 |
Oblak, Polona, matematika | 22723 |
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