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Communications in Algebra Volume 42, 2014 - Issue 2
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Original Articles

PBW-Pairs of Varieties of Linear Algebras

Alexander A. Mikhalev Department of Mechanics and Mathematics, Moscow State University, Moscow, RussiaCorrespondence[email protected]
&
Ivan P. Shestakov Instituto de Matemática e Estatística, Universidade de S\ ao Paulo, Caixa, Sao Paulo, Braziland Sobolev Institute of Mathematics, Novosibirsk, Russia
Pages 667-687 | Received 12 Jun 2012, Published online: 18 Oct 2013

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Xiao-Song Peng, Yi Zhang, Xing Gao & Yan-Feng Luo. (2022) Universal enveloping of (modified) λ-differential Lie algebras. Linear and Multilinear Algebra 70:6, pages 1102-1127.
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Yu Li, Qiuhui Mo & L. A. Bokut. (2020) Generalized anti-commutative Gröbner-Shirshov basis theory and free Sabinin algebras. Communications in Algebra 48:12, pages 5086-5109.
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Vladimir Dotsenko. (2020) Functorial PBW theorems for post-Lie algebras. Communications in Algebra 48:5, pages 2072-2080.
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Yu Li, Qiuhui Mo & Xiangui Zhao. (2019) The Freiheitssatz and automorphisms for free brace algebras. Communications in Algebra 47:10, pages 4125-4136.
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Pavel Kolesnikov. (2017) Gröbner–Shirshov bases for pre-associative algebras. Communications in Algebra 45:12, pages 5283-5296.
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F. A. Mashurov & B. K. Sartayev. (2022) Metabelian Lie and perm algebras. Journal of Algebra and Its Applications 23:04.
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VLADIMIR DOTSENKO & OISÍN FLYNN-CONNOLLY. (2023) Three Schur functors related to pre-Lie algebras. Mathematical Proceedings of the Cambridge Philosophical Society 176:2, pages 441-458.
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Vladimir Dotsenko & Ualbai Umirbaev. (2023) An Effective Criterion for Nielsen–Schreier Varieties. International Mathematics Research Notices 2023:23, pages 20385-20432.
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Bauyrzhan Sartayev & Pavel Kolesnikov. (2023) Noncommutative Novikov algebras. European Journal of Mathematics 9:2.
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Vladimir Dotsenko, Nurlan Ismailov & Ualbai Umirbaev. (2023) Polynomial identities in Novikov algebras. Mathematische Zeitschrift 303:3.
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L. S. I. Murakami, L. A. Peresi & I. P. Shestakov. (2021) A retrospect of the research in nonassociative algebras in IME-USP. São Paulo Journal of Mathematical Sciences 16:1, pages 84-130.
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Yuqun Chen, Ivan Shestakov & Zerui Zhang. (2022) Free Lie-admissible algebras and an analogue of the PBW theorem. Journal of Algebra 590, pages 234-253.
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N. A. Ismailov & A. S. Dzhumadil’daev. (2021) Binary Leibniz Algebras. Mathematical Notes 110:3-4, pages 322-328.
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Vladimir Dotsenko & Pedro Tamaroff. (2021) Endofunctors and Poincaré–Birkhoff–Witt Theorems. International Mathematics Research Notices 2021:16, pages 12670-12690.
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Nurlan A Ismailov & Askar Serkulovich Dzhumadil'daev. (2021) Бинарно-лейбницевы алгебрыBinary Leibniz Algebras. Математические заметки Matematicheskie Zametki 110:3, pages 336-344.
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Vsevolod Gubarev. (2020) Embedding of Pre-Lie Algebras into Preassociative Algebras. Algebra Colloquium 27:02, pages 299-310.
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P.S. Kolesnikov, B. Sartayev & A. Orazgaliev. (2019) Gelfand–Dorfman algebras, derived identities, and the Manin product of operads. Journal of Algebra 539, pages 260-284.
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Qiuhui Mo. (2019) Embedding Theorems for L -Algebras and Anti-commutative Algebras . Algebra Colloquium 26:01, pages 51-64.
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V. Yu. Gubarev. (2019) Universal Enveloping Lie Rota–Baxter Algebras of Pre-Lie and Post-Lie Algebras. Algebra and Logic 58:1, pages 1-14.
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I. A. Groo. (2019) A Linear Basis of the Free Akivis Algebra. Journal of Mathematical Sciences 237:2, pages 280-283.
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V. A. Artamonov, A. V. Klimakov, A. A. Mikhalev & A. V. Mikhalev. (2019) Primitive and Almost Primitive Elements of Schreier Varieties. Journal of Mathematical Sciences 237:2, pages 157-179.
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V. Gubarev. (2018) Universal enveloping associative Rota–Baxter algebras of preassociative and postassociative algebra. Journal of Algebra 516, pages 298-328.
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Vsevolod Gubarev. (2017) Universal Enveloping Commutative Rota–Baxter Algebras of Pre- and Post-Commutative Algebras. Axioms 6:4, pages 33.
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P.S. Kolesnikov. (2017) Gröbner–Shirshov Bases for Replicated Algebras. Algebra Colloquium 24:04, pages 563-576.
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Yu Li & Qiuhui Mo. (2017) On Free Pre-Lie Algebras. Algebra Colloquium 24:02, pages 267-284.
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