Roots of unity as a Lie algebra

A. Davydov, R. Street

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)


    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
    Issue number4
    Publication statusPublished - 2002


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


    Dive into the research topics of 'Roots of unity as a Lie algebra'. Together they form a unique fingerprint.

    Cite this