Representations of polynomial Rota–Baxter algebras

@article{Qiao2017RepresentationsOP,
  title={Representations of polynomial Rota–Baxter algebras},
  author={Li Qiao and Jun Pei},
  journal={Journal of Pure and Applied Algebra},
  year={2017}
}
  • Li QiaoJun Pei
  • Published 8 August 2017
  • Mathematics
  • Journal of Pure and Applied Algebra
View PDF on arXiv
12 Citations
Highly Influential Citations
1
Background Citations
7
Methods Citations
4

12 Citations

Representations and modules of Rota–Baxter algebras

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Modules of polynomial Rota-Baxter Algebras and matrix equations

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Rota-Baxter Modules Toward Derived Functors

In this paper we study Rota-Baxter modules with emphasis on the role played by the Rota-Baxter operators and the resulting difference between Rota-Baxter modules and the usual modules over an…

Rota-Baxter Modules Toward Derived Functors

In this paper we study Rota-Baxter modules with emphasis on the role played by the Rota-Baxter operators and the resulting difference between Rota-Baxter modules and the usual modules over an…

Monomial Rota-Baxter operators of nonzero weight on $F[x,y]$ coming from averaging operators

The intensive study of Rota—Baxter operators on the polynomial algebra F [ x ] has been started with the work of S.H. Zheng, L. Guo, and M. Rosenkranz (2015). We deal with the case of two variables…

Representations and cohomologies of relative Rota-Baxter Lie algebras and applications

Factorizable Lie Bialgebras, Quadratic Rota–Baxter Lie Algebras and Rota–Baxter Lie Bialgebras

In this paper, first we introduce the notion of quadratic Rota–Baxter Lie algebras of arbitrary weight, and show that there is a one-to-one correspondence between factorizable Lie bialgebras and…

Injective Rota–Baxter Operators of Weight Zero on F[x]

Rota–Baxter operators present a natural generalization of integration by parts formula for the integral operator. In 2015, Zheng, Guo, and Rosenkranz conjectured that every injective Rota–Baxter…

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There is a Rota-Baxter algebra structure on the field $A=\mathbf{k}((t))$ with $ P$ being the projection map $A=\mathbf{k}[[t]]\oplus t^{-1}\mathbf{k}[t^{-1}]$ onto $ \mathbf{k}[[ t]]$. We study the…

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An Ore extension over a polynomial algebra F[x] is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra A_h generated by elements x,y, which satisfy…

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An Ore extension over a polynomial algebra F[x] is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra Ah generated by elements x, y, which satisfy…

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