1. Home
    2. Journals
    3. Proceedings – Mathematical Sciences
    4. Volume 133
    5. All articles

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/133/0004

    • 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

       

      VALERIY G BARDAKOV1 2 3 4 VSEVOLOD GUBAREV1 2

      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

       
      Published
      28 February 2023
      Manuscript received
      12 July 2022
      Manuscript revised
      12 October 2022
      Accepted
      20 November 2022
      Final version published online
      28 February 2023

  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2022-2023 Indian Academy of Sciences, Bengaluru.

Contact | Site index