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Maximal Nilpotent Subalgebras II - A correspondence theorem within solvable associative algebras. With 242 exercises

2017, Pocket, Engelsk

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Within series II we extend the theory of maximal nilpotent substructures to solvable associative algebras, especially for their group of units and their associated Lie algebra.We construct all maximal nilpotent Lie subalgebras and characterize them by simple and double centralizer properties. They possess distinctive attractor and repeller characteristics. Their number of isomorphic classes is finite and can be bounded by Bell numbers. Cartan subalgebras and the Lie nilradical are extremal among all maximal nilpotent Lie subalgebras.The maximal nilpotent Lie subalgebras are connected to the maximal nilpotent subgroups. This correspondence is bijective via forming the group of units and creating the linear span. Cartan subalgebras and Carter subgroups as well as the Lie nilradical and the Fitting subgroup are linked by this correspondence. All partners possess the same class of nilpotency based on a theorem of Xiankun Du.By using this correspondence we transfer all results to maximal ni

Produktegenskaper

  • Forfatter

  • Bidragsyter

    Wirsing, Sven Bodo
  • Forlag/Utgiver

    SD Books
  • Format

    Pocket
  • Språk

    Engelsk
  • Utgivelsesår

    2017
  • Antall sider

    196
  • Varenummer

    9783960671961

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