Roots of unity as a Lie algebra

A. Davydov, R. Street

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    1 Citation (Scopus)

    Abstract

    This note gives a categorical development arising from a theorem of A. A. Klyachko relating the Lie operad to roots of unity. We examine the "substitude" structure on the groupoid C whose homsets are the cyclic groups. The roots of unity representations of the cyclic groups form a Lie algebra for a certain oplax monoidal structure on the category of linear representations of C.
    Original languageEnglish
    Pages (from-to)683-690
    Number of pages8
    JournalGeorgian Mathematical Journal
    Volume9
    Issue number4
    Publication statusPublished - 2002

    Keywords

    • Lie algebra
    • operad
    • substitude
    • species
    • cyclic group

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