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    • Keywords


      Rota--Baxter operator; Rota--Baxter group; simple group; sporadic group; factorization.

    • Abstract


      The theory of Rota--Baxter operators on rings and algebras has been developed since 1960. In 2020, the notion of Rota--Baxter operator on a group was defined. Further, it was proved that one may define a skew left brace on any group endowed with a Rota--Baxter operator. Thus, a group endowed with a Rota--Baxter operator gives rise to a set-theoretical solution to the Yang--Baxter equation. We provide some general constructions of Rota--Baxter operators on a group. Given a map on a group, we study its extensions to a Rota--Baxter operator. We state the connection between Rota--Baxter operators on a group and Rota--Baxter operators on an associated Lie ring. We describe Rota--Baxter operators on sporadic simple groups.

    • Author Affiliations



      1. Sobolov Institute of Mathematics, Acad. Koptyug Ave. 4, 630090 Novosibirsk, Russia
      2. Novosibirsk State University, Pirogova str. 2, 630090 Novosibirsk, Russia
      3. Novosibirsk State Agrarian University, Dobrolyubova str., 160, 630039 Novosibirsk, Russia
      4. Regional Scientific and Educational Mathematical Center of Tomsk State University, Lenin ave., 36, 634009, Tomsk, Russia
    • Dates

  • Proceedings – Mathematical Sciences | News

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