• Corpus ID: 219303715

Spectrum of Rota-Baxter operators

@article{Gubarev2020SpectrumOR,
  title={Spectrum of Rota-Baxter operators},
  author={Vsevolod Gubarev},
  journal={arXiv: Rings and Algebras},
  year={2020}
}
  • V. Gubarev
  • Published 4 June 2020
  • Mathematics
  • arXiv: Rings and Algebras
We prove that the spectrum of every Rota-Baxter operator of weight $\lambda$ on a unital algebraic (not necessarily associative) algebra over a field of characteristic zero is a subset of $\{0,-\lambda\}$. For a finite-dimensional unital algebra the same statement is shown to hold without a restriction on the characteristic of the ground field. Based on these results, we define the Rota-Baxter $\lambda$-index $\mathrm{rb}_\lambda(A)$ of an algebra $A$ as the infimum of the degrees of minimal… 

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