Rota-Baxter operators on Turaev's Hopf group (co)algebras I: Basic definitions and related algebraic structures
نویسندگان
چکیده
We find a natural compatible condition between the Rota-Baxter operator and Turaev's (Hopf) group-(co)algebras, which leads to concept of group-(co)algebra. Two characterizations group-algebras (abbr. T-algebras) are obtained: one by Atkinson factorization other T-quasi-idempotent elements. The relations among some related group algebraic structures (such as (tri)dendriform T-algebras, Zinbiel pre-Lie Lie discussed, concrete examples from algebras dimensions 2,3 4 given. At last we prove that Poisson T-algebras can produce pre-Poisson be obtained T-algebras.
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2022
ISSN: ['1879-1662', '0393-0440']
DOI: https://doi.org/10.1016/j.geomphys.2022.104469