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This article is cited in 6 scientific papers (total in 6 papers)
Rota–Baxter operators on unital algebras
V. Gubarevab a University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
b Sobolev Institute of Mathematics, Acad. Koptyug ave. 4, 630090 Novosibirsk, Russia
Abstract:
We state that all Rota–Baxter operators of nonzero weight on the Grassmann algebra over a field of characteristic zero are projections 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 $M_n(F)$ (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 $\mathrm{rb}(A)$ as the minimal nilpotency index of Rota–Baxter operators of weight zero on $A$. We show that $\mathrm{rb}(M_n(F)) = 2n-1$ provided that characteristic of $F$ is zero.
Key words and phrases:
rota–Baxter operator, Yang–Baxter equation, matrix algebra, Grassmann algebra, Faulhaber polynomial.
Citation:
V. Gubarev, “Rota–Baxter operators on unital algebras”, Mosc. Math. J., 21:2 (2021), 325–364
Linking options:
https://www.mathnet.ru/eng/mmj795 https://www.mathnet.ru/eng/mmj/v21/i2/p325
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