L. A. Bokut, Yu. Chen, X. Deng, “Gröbner–Shirshov bases for Rota–Baxter algebras”, Sibirsk. Mat. Zh., 51:6 (2010), 1237–1250; Siberian Math. J., 51:6 (2010), 978

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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 6, Pages 1237–1250 (Mi smj2158)

This article is cited in 28 scientific papers (total in 28 papers)

Gröbner–Shirshov bases for Rota–Baxter algebras

L. A. Bokut^ab, Yu. Chen^b, X. Deng^b

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b South China Normal University, Guangzhou, Republic of China

Full-text PDF (358 kB) Citations (28)

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Abstract: We establish the composition-diamond lemma for associative nonunitary Rota–Baxter algebras of weight

λ

$\lambda$ . To give an application, we construct a linear basis for a free commutative and nonunitary Rota–Baxter algebra, show that every countably generated Rota–Baxter algebra of weight 0 can be embedded into a two-generated Rota–Baxter algebra, and prove the 1-PBW theorems for dendriform dialgebras and trialgebras.

Keywords: Rota–Baxter algebra, Gröbner–Shirshov basis.

Received: 15.09.2009

English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 6, Pages 978–988
DOI: https://doi.org/10.1007/s11202-010-0097-1

Bibliographic databases:

Document Type: Article

UDC: 510.53+512.552.4+512.579+519.117

Language: Russian

Citation: L. A. Bokut, Yu. Chen, X. Deng, “Gröbner–Shirshov bases for Rota–Baxter algebras”, Sibirsk. Mat. Zh., 51:6 (2010), 1237–1250; Siberian Math. J., 51:6 (2010), 978–988

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/smj2158

https://www.mathnet.ru/eng/smj/v51/i6/p1237

This publication is cited in the following 28 articles:

Huizhen Qiu, Shanghua Zheng, Yangfan Dan, “Construction of free quasi-idempotent differential Rota-Baxter algebras by Gröbner-Shirshov bases”, Communications in Algebra, 52:6 (2024), 2404
François Lemaire, Louis Roussel, Lecture Notes in Computer Science, 14938, Computer Algebra in Scientific Computing, 2024, 215
François Lemaire, Louis Roussel, “A Prototype for Integral Elimination”, ACM Commun. Comput. Algebra, 58:3 (2024), 93
V. Gubarev, “Rota–Baxter operators on unital algebras”, Mosc. Math. J., 21:2 (2021), 325–364
Chen D., Luo Ya.-F., Zhang Y., Zhang Yu.-Yu., “Free Omega-Rota-Baxter Algebras and Grobner-Shirshov Bases”, Int. J. Algebr. Comput., 30:7 (2020), 1359–1373
Li Yu., Mo Q., Bokut L.A., “Generalized Anti-Commutative Grobner-Shirshov Basis Theory and Free Sabinin Algebras”, Commun. Algebr., 48:12 (2020), 5086–5109
Gubarev V., “Embedding of Pre-Lie Algebras Into Preassociative Algebras”, Algebr. Colloq., 27:2 (2020), 299–310
Gubarev V., “Poincare-Birkhoff-Witt Theorem For Pre-Lie and Post-Lie Algebras”, J. Lie Theory, 30:1 (2020), 223–238
Tuniyaz R., Obul A., “Grobner-Shirshov Basis Method For Multiple Tensor Products of Some Associative Algebras”, Asian-Eur. J. Math., 12:1 (2019), 1950015
Gubarev V., “Universal Enveloping Associative Rota-Baxter Algebras of Preassociative and Postassociative Algebra”, J. Algebra, 516 (2018), 298–328
Li Yu., Mo Q., Zhao X., “Grobner-Shirshov Bases For Brace Algebras”, Commun. Algebr., 46:11 (2018), 4577–4589
Tuniyaz R., Bokut L.A., Xiryazidin M., Obul A., “Grobner-Shirshov Bases For Free Gelfand-Dorfman-Novokov Algebras and For Right Ideals of Free Right Leibniz Algebras”, Commun. Algebr., 46:10 (2018), 4392–4402
Li Yu., Mo Q., “Embedding Into 2-Generated Simple Associative (Lie) Algebras”, Commun. Algebr., 45:6 (2017), 2435–2443
Yu. Chen, Y. Li, Q. Tang, “Gröbner–Shirshov bases for some Lie algebras”, Siberian Math. J., 58:1 (2017), 176–182
V. Yu. Gubarev, “Free Lie Rota–Baxter algebras”, Siberian Math. J., 57:5 (2016), 809–818
Gao X., Guo L., Rosenkranz M., “Free Integro-Differential Algebras and Grobner Shirshov Bases”, J. Algebra, 442:SI (2015), 354–396
Zheng Sh., Guo L., “Relative Locations of Subwords in Free Operated Semigroups and Motzkin Words”, Front. Math. China, 10:5 (2015), 1243–1261
Bokut L.A., Chen Yu., Chen W., Li J., “New Approaches To Plactic Monoid Via Grobner-Shirshov Bases”, J. Algebra, 423 (2015), 301–317
Gao X., Guo L., Zheng Sh., “Construction of Free Commutative Integro-Differential Algebras by the Method of Grobner-Shirshov Bases”, J. Algebra. Appl., 13:5 (2014), 1350160
Bokut L.A., Chen Yu., “Grobner-Shirshov Bases and Their Calculation”, Bull. Math. Sci., 4:3 (2014), 325–395

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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