Free Ω-Rota–Baxter algebras and Gröbner–Shirshov bases
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Publication:4970533
DOI10.1142/S0218196720500447zbMath1469.16084OpenAlexW3046684283MaRDI QIDQ4970533
Dan Chen, Yi Zhang, Yuanyuan Zhang, Yan-Feng Luo
Publication date: 14 October 2020
Published in: International Journal of Algebra and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0218196720500447
Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Free algebras (08B20) Associative rings and algebras with additional structure (16W99) Yang-Baxter equations and Rota-Baxter operators (17B38) Gröbner-Shirshov bases (16Z10)
Related Items (2)
Rota-Baxter operators on Turaev's Hopf group (co)algebras. I: Basic definitions and related algebraic structures ⋮ Matching Hom-setting of Rota-Baxter algebras, dendriform algebras, and pre-Lie algebras
Cites Work
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- Rota-Baxter systems, dendriform algebras and covariant bialgebras
- Rota's classification problem, rewriting systems and Gröbner-Shirshov bases
- \(\mathcal O\)-operators on associative algebras and associative Yang-Baxter equations.
- Free integro-differential algebras and Gröbner-Shirshov bases.
- Algebraic Birkhoff factorization and the Euler-Maclaurin formula on cones
- Gröbner-Shirshov bases for Rota-Baxter algebras.
- Polylogarithms and multiple zeta values from free Rota-Baxter algebras
- An analytic problem whose solution follows from a simple algebraic identity
- Operated semigroups, Motzkin paths and rooted trees
- Gröbner-Shirshov bases for associative algebras with multiple operators and free Rota-Baxter algebras.
- Hopf algebras, renormalization and noncommutative geometry
- Composition-diamond lemma for associative conformal algebras.
- Splitting of operads and Rota-Baxter operators on operads
- On free Gelfand-Dorfman-Novikov-Poisson algebras and a PBW theorem
- Loday-type algebras and the Rota-Baxter relation
- Differential type operators and Gröbner-Shirshov bases.
- Baxter algebras and shuffle products
- Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
- Rota-Baxter algebras and dendriform algebras.
- A Lie theoretic approach to renormalization
- Mixable shuffles, quasi-shuffles and Hopf algebras.
- Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras
- $\mathcal{O}$-OPERATORS ON ASSOCIATIVE ALGEBRAS, ASSOCIATIVE YANG-BAXTER EQUATIONS AND DENDRIFORM ALGEBRAS
- Baxter algebras and combinatorial identities. II
- Baxter algebras and Hopf algebras
- Free Rota-Baxter systems and a Hopf algebra structure
- Gröbner–Shirshov bases for pre-associative algebras
- Gröbner–Shirshov Bases for Replicated Algebras
- Free Lie differential Rota–Baxter algebras and Gröbner–Shirshov bases
- Some new results on Gröbner–Shirshov bases for Lie algebras and around
- Spitzer's identity and the algebraic Birkhoff decomposition in pQFT
- Generalizations of the classical Yang-Baxter equation and ${\mathcal O}$O-operators
- Gröbner-Shirshov bases for free Gelfand-Dorfman-Novokov algebras and for right ideals of free right Leibniz algebras
- Rota-Baxter operators on $\mathrm{sl(2,\mathbb {C})}$ sl (2,C) and solutions of the classical Yang-Baxter equation
- From Rota–Baxter algebras to pre-Lie algebras
- Pre-Poisson algebras
- On the associative analog of Lie bialgebras
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