Gröbner–Shirshov bases for Lie Ω-algebras and free Rota–Baxter Lie algebras
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Publication:4588382
DOI10.1142/S0219498817501900zbMath1384.16016arXiv1604.06675WikidataQ115245634 ScholiaQ115245634MaRDI QIDQ4588382
Publication date: 26 October 2017
Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1604.06675
Gröbner-Shirshov basisLyndon-Shirshov wordRota-Baxter Lie algebraLie {\(\Omega\)}-algebraNijenhuis Lie algebra
Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Free nonassociative algebras (17A50) Yang-Baxter equations (16T25)
Related Items
Operator identities on Lie algebras, rewriting systems and Gröbner-Shirshov bases ⋮ Free Lie differential Rota–Baxter algebras and Gröbner–Shirshov bases ⋮ Some new results on Gröbner–Shirshov bases for Lie algebras and around ⋮ Unnamed Item ⋮ Universal enveloping Lie Rota-Baxter algebras of pre-Lie and post-Lie algebras ⋮ Universal enveloping commutative Rota-Baxter algebras of pre- and post-commutative algebras ⋮ Universal enveloping associative Rota-Baxter algebras of preassociative and postassociative algebra
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Cites Work
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- Free integro-differential algebras and Gröbner-Shirshov bases.
- Nijenhuis algebras, NS algebras, and N-dendriform algebras.
- Generalized Lax pairs, the modified classical Yang-Baxter equation, and affine geometry of Lie groups
- Die Unterringe der freien Lieschen Ringe
- An analytic problem whose solution follows from a simple algebraic identity
- What is a classical r-matrix?
- Combinatorics of the free Baxter algebra
- Gröbner-Shirshov bases for Lie algebras: after A. I. Shirshov
- Selected works of A. I. Shirshov. Translated by Murray Bremner and Mikhail V. Kotchetov. Edited by Leonid A. Bokut, Victor Latyshev, Ivan Shestakov and Efim Zelmanov
- Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras
- Gröbner bases for operads
- Twisting on associative algebras and Rota-Baxter type operators.
- Operated semigroups, Motzkin paths and rooted trees
- Gröbner-Shirshov bases for associative algebras with multiple operators and free Rota-Baxter algebras.
- The diamond lemma for ring theory
- Gröbner-Shirshov bases: from their inception to the present time.
- Loday-type algebras and the Rota-Baxter relation
- On the associative Nijenhuis relation
- Baxter algebras and shuffle products
- On free Baxter algebras: Completions and the internal construction
- Rota-Baxter operators on pre-Lie superalgebras
- Rota-Baxter algebras and dendriform algebras.
- On differential Rota-Baxter algebras.
- Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
- On the structure of free Baxter algebras
- Resolution of singularities of an algebraic variety over a field of characteristic zero. I
- GRÖBNER–SHIRSHOV BASES AND EMBEDDINGS OF ALGEBRAS
- Groups with Multiple Operators
- FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES
- COMPOSITION-DIAMOND LEMMA FOR λ-DIFFERENTIAL ASSOCIATIVE ALGEBRAS WITH MULTIPLE OPERATORS
- Rota-Baxter operators on pre-Lie algebras
- Planar trees, free nonassociative algebras, invariants, and elliptic integrals
- QUANTUM BI-HAMILTONIAN SYSTEMS
- Groebner-Shirshov basis of the universal enveloping Rota-Baxter algebra of a Lie algebra
- A Contribution to the Theory of Groups of Prime-Power Order
- Some New Results on Gröbner-Shirshov Bases
- GRÖBNER–SHIRSHOV BASES FOR L-ALGEBRAS
- Gröbner–Shirshov bases and their calculation
- 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
- Baxter algebras and combinatorial identities. I
- A Basis for Free Lie Rings and Higher Commutators in Free Groups
- On the Representation of Lie Rings in Associative Rings
- Free differential calculus. IV: The quotient groups of the lower central series
