Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Bardakov, V. G., Bovdi, V. A.
Institution: United Arab Emirates University
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4391984892