Rota–Baxter Operators on Skew Braces

Ximu Wang, Chongxia Zhang and Liangyun Zhang ()
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Ximu Wang: Department of Mathematics, Nanjing Agricultural University, Nanjing 210095, China
Chongxia Zhang: Department of Mathematics, Nanjing Agricultural University, Nanjing 210095, China
Liangyun Zhang: Department of Mathematics, Nanjing Agricultural University, Nanjing 210095, China

Mathematics, 2024, vol. 12, issue 11, 1-14

Abstract: In this paper, we introduce the concept of Rota–Baxter skew braces, and provide classifications of Rota–Baxter operators on various skew braces, such as ( Z , + , ∘ ) and ( Z / ( 4 ) , + , ∘ ) . We also present a necessary and sufficient condition for a skew brace to be a co-inverse skew brace. Additionally, we describe some constructions of Rota–Baxter quasiskew braces, and demonstrate that every Rota–Baxter skew brace can induce a quasigroup and a Rota–Baxter quasiskew brace.

Keywords: Rota–Baxter operator; skew brace; co-inverse skew brace; Rota–Baxter quasiskew brace (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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