Rota–baxter operators on unital algebras Full article
| Journal |
Moscow Mathematical Journal
ISSN: 1609-3321 |
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| Output data | Year: 2021, Volume: 21, Number: 2, Pages: 325-364 Pages count : 40 DOI: 10.17323/1609-4514-2021-21-2-325-364 | ||||
| Tags | Faulhaber polynomial; Grassmann algebra; Matrix algebra; Rota–Baxter operator; Yang–Baxter equation | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | 0314-2019-0001 |
Abstract:
We state that all Rota–Baxter operators of nonzero weight on the Grassmann algebra over a field of characteristic zero are pro-jections on a subalgebra along another one. We show the one-to-one correspondence between the solutions of associative Yang–Baxter equation and Rota–Baxter operators of weight zero on the matrix algebra Mn(F ) (joint with P. Kolesnikov). We prove that all Rota–Baxter operators of weight zero on a unital associative (alternative, Jordan) algebraic algebra over a field of characteristic zero are nilpotent. We introduce a new invariant for an algebra A called the RB-index rb(A) as the minimal nilpotency index of Rota– Baxter operators of weight zero on A. We show that rb(Mn(F )) = 2n−1 provided that characteristic of F is zero. © 2021 Independent University of Moscow.
Cite:
Gubarev V.
Rota–baxter operators on unital algebras
Moscow Mathematical Journal. 2021. V.21. N2. P.325-364. DOI: 10.17323/1609-4514-2021-21-2-325-364 WOS Scopus OpenAlex
Rota–baxter operators on unital algebras
Moscow Mathematical Journal. 2021. V.21. N2. P.325-364. DOI: 10.17323/1609-4514-2021-21-2-325-364 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000663354100004 |
| Scopus: | 2-s2.0-85105351833 |
| OpenAlex: | W3155837056 |