Free Rota-Baxter family algebras and (tri)dendriform family algebras
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Publication:2305362
DOI10.2140/pjm.2019.301.741OpenAlexW2981588195WikidataQ126983901 ScholiaQ126983901MaRDI QIDQ2305362
Publication date: 10 March 2020
Published in: Pacific Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2140/pjm.2019.301.741
Gröbner-Shirshov basisRota-Baxter algebraRota-Baxter family algebradendriform family algebratridendriform family algebra
Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) 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)
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Cites Work
- Unnamed Item
- Unnamed Item
- 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
- An analytic problem whose solution follows from a simple algebraic identity
- New identities in dendriform algebras
- 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
- Leibniz homology of dialgebras of matrices
- Arithmetree.
- 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
- On free Baxter algebras: Completions and the internal construction
- Rota-Baxter algebras and dendriform algebras.
- On differential Rota-Baxter algebras.
- A Lie theoretic approach to renormalization
- On the structure of free Baxter algebras
- Some aspects of Baxter's functional equation
- Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras
- A Combinatorial Lemma and Its Application to Probability Theory
- Baxter algebras and combinatorial identities. II
- Spitzer's identity and the algebraic Birkhoff decomposition in pQFT
- Gröbner–Shirshov bases and their calculation
- Splitting of Operations, Manin Products, and Rota–Baxter Operators
- CONSTRUCTION OF FREE COMMUTATIVE INTEGRO-DIFFERENTIAL ALGEBRAS BY THE METHOD OF GRÖBNER–SHIRSHOV BASES
- From Rota–Baxter algebras to pre-Lie algebras
- Baxter algebras and combinatorial identities. I
- Pre-Poisson algebras
- On the associative analog of Lie bialgebras
