Spectrum of Rota - Baxter Operators Full article
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International Journal of Algebra and Computation
ISSN: 0218-1967 , E-ISSN: 1793-6500 |
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| Output data | Year: 2025, Pages: 1-26 Pages count : 26 DOI: 10.1142/s0218196725500195 | ||||
| Tags | Rota–Baxter operator; matrix algebra; associative Yang–Baxter equation; Rota–Baxter module | ||||
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Abstract:
Rota–Baxter operators have been studied since 1960, and there are lots of their applications in mathematical physics, number theory, and noncommutative geometry. We state a surprisingly general property of such operators: the spectrum of every Rota–Baxter operator of weight λ on a finite-dimensional unital (not necessarily associative) algebra is a subset of {0,−λ}. We even extend this result to the case of infinite-dimensional algebraic algebras (when charF = 0). Based on these results, we define a new invariant of an algebra: the Rota–Baxter λ-index rbλ(A)ofanalgebraA as the infimum of the degrees of minimal polynomials of all Rota–Baxter operators of weight λ on A.Wecompute the Rota–Baxter λ-index for the matrix algebra Mn(F), charF =0: it is shown that rbλ(Mn(F)) = 2n−1.
Cite:
Gubarev V.
Spectrum of Rota - Baxter Operators
International Journal of Algebra and Computation. 2025. P.1-26. DOI: 10.1142/s0218196725500195 WOS Scopus OpenAlex
Spectrum of Rota - Baxter Operators
International Journal of Algebra and Computation. 2025. P.1-26. DOI: 10.1142/s0218196725500195 WOS Scopus OpenAlex
Dates:
| Submitted: | Aug 13, 2024 |
| Accepted: | Apr 23, 2025 |
| Published online: | Jun 6, 2025 |
Identifiers:
| Web of science: | WOS:001503610900001 |
| Scopus: | 2-s2.0-105007533210 |
| OpenAlex: | W3034093496 |
Citing:
| DB | Citing |
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| OpenAlex | 3 |