2024/02/18 by В. Г. Бардаков, Bardakov, V. G., Victor Bovdi +1 · 1 citation
Computer Science · Mathematics · #17A30 #20E22 #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2402.11660
openalex publication_date 2024/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present article we define and investigate relative Rota--Baxter operators and relative averaging operators on racks and rack algebras. Also, if B is a Rota--Baxter or averaging operator on a rack X, then we can extend B by linearity to the rack algebra k[X]. On the other side, we have definitions of Rota--Baxter and averaging operators on arbitrary algebra. We find connections between these operators. In particular, we prove that if B : X --> X is an averaging operator on a rack, then its linear extension on a rack algebra k[X] gives an averaging operator.