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Algebra Logika, 2011, Volume 50, Number 5, Pages 595–614 (Mi al504)  

This article is cited in 11 scientific papers (total in 11 papers)

Bases for partially commutative Lie algebras

E. N. Poroshenko

Novosibirsk State Technical University, Novosibirsk, Russia

Abstract: We give an explicit description of linear bases for partially commutative Lie algebras. To do this, use is made of the Gröbner–Shirshov basis method.

Keywords: partially commutative Lie algebra, linear basis, Gröbner–Shirshov basis.

Full text: PDF file (225 kB)
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English version:
Algebra and Logic, 2011, 50:5, 405–417

Bibliographic databases:

UDC: 512.554.33
Received: 10.12.2010
Revised: 11.04.2011

Citation: E. N. Poroshenko, “Bases for partially commutative Lie algebras”, Algebra Logika, 50:5 (2011), 595–614; Algebra and Logic, 50:5 (2011), 405–417

Citation in format AMSBIB
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\paper Bases for partially commutative Lie algebras
\jour Algebra Logika
\yr 2011
\vol 50
\issue 5
\pages 595--614
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\jour Algebra and Logic
\yr 2011
\vol 50
\issue 5
\pages 405--417
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. N. Poroshenko, “Centralizers in partially commutative Lie algebras”, Algebra and Logic, 51:4 (2012), 351–371  mathnet  crossref  mathscinet  zmath  isi
    2. E. N. Poroshenko, E. I. Timoshenko, “Universal equivalence of partially commutative metabelian Lie algebras”, J. Algebra, 384 (2013), 143–168  crossref  mathscinet  zmath  isi  elib  scopus
    3. Leonid A. Bokut, Yuqun Chen, “Gröbner–Shirshov bases and PBW theorems”, Zhurn. SFU. Ser. Matem. i fiz., 6:4 (2013), 417–427  mathnet
    4. V. Yu. Gubarev, “Simple associative $\Gamma$-conformal algebras of finite type for a torsion-free group $\Gamma$”, Algebra and Logic, 52:5 (2013), 371–386  mathnet  crossref  mathscinet  isi
    5. L. A. Bokut, Yu. Chen, “Gröbner–Shirshov bases and their calculation”, Bull. Math. Sci., 4:3 (2014), 325–395  crossref  mathscinet  zmath  isi  elib  scopus
    6. E. N. Poroshenko, “On universal equivalence of partially commutative metabelian Lie algebras”, Commun. Algebr., 43:2 (2015), 746–762  crossref  mathscinet  zmath  isi  elib  scopus
    7. V. Yu. Gubarev, “Free Lie Rota–Baxter algebras”, Siberian Math. J., 57:5 (2016), 809–818  mathnet  crossref  crossref  isi  elib  elib
    8. I. Kaygorodov, “Algebras of Jordan brackets and generalized Poisson algebras”, Linear Multilinear Algebra, 65:6 (2017), 1142–1157  crossref  mathscinet  zmath  isi  scopus
    9. E. N. Poroshenko, “Universal equivalence of partially commutative Lie algebras”, Algebra and Logic, 56:2 (2017), 133–148  mathnet  crossref  crossref  isi
    10. E. N. Poroshenko, “Universal equivalence of some countably generated partially commutative structures”, Siberian Math. J., 58:2 (2017), 296–304  mathnet  crossref  crossref  isi  elib  elib
    11. G. Arunkumar, D. Kus, R. Venkatesh, “Root multiplicities for Borcherds algebras and graph coloring”, J. Algebra, 499 (2018), 538–569  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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