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Mat. Sb. (N.S.), 1985, Volume 127(169), Number 4(8), Pages 476–482 (Mi msb2008)  

This article is cited in 31 scientific papers (total in 31 papers)

Deformations of Lie algebras

A. Fialowski


Abstract: The author considers general questions of deformations of Lie algebras over a field of characteristic zero, and the related problems of computing cohomology with coefficients in adjoint representations. The construction of a versal family, and the construction of obstructions to the extension of deformations, are also considered.
Bibliography: 13 titles.

Full text: PDF file (522 kB)
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English version:
Mathematics of the USSR-Sbornik, 1986, 55:2, 467–473

Bibliographic databases:

UDC: 517.986
MSC: Primary 17B56; Secondary 13D03
Received: 07.05.1984

Citation: A. Fialowski, “Deformations of Lie algebras”, Mat. Sb. (N.S.), 127(169):4(8) (1985), 476–482; Math. USSR-Sb., 55:2 (1986), 467–473

Citation in format AMSBIB
\Bibitem{Fia85}
\by A.~Fialowski
\paper Deformations of Lie algebras
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 127(169)
\issue 4(8)
\pages 476--482
\mathnet{http://mi.mathnet.ru/msb2008}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=806511}
\zmath{https://zbmath.org/?q=an:0597.17010|0583.17010}
\transl
\jour Math. USSR-Sb.
\yr 1986
\vol 55
\issue 2
\pages 467--473
\crossref{https://doi.org/10.1070/SM1986v055n02ABEH003014}


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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. Alice Fialowski, “Deformations of some infinite-dimensional Lie algebras”, J Math Phys (N Y ), 31:6 (1990), 1340  crossref  mathscinet  zmath
    2. Fialowski A., Ohalloran J., “A Comparison of Deformations and Orbit Closure”, Commun. Algebr., 18:12 (1990), 4121–4140  mathscinet  zmath  isi
    3. Alice Fialowski, Dmitry Fuchs, “Construction of Miniversal Deformations of Lie Algebras”, Journal of Functional Analysis, 161:1 (1999), 76  crossref
    4. Alice Fialowski, Gerhard Post, “Versal Deformation of the Lie Algebra L2”, Journal of Algebra, 236:1 (2001), 93  crossref
    5. Dmitry Fuchs, Lynelle Lang Weldon, “Massey brackets and deformations”, Journal of Pure and Applied Algebra, 156:2-3 (2001), 215  crossref
    6. Alice Fialowski, Michael Penkava, “Deformation theory of infinity algebras”, Journal of Algebra, 255:1 (2002), 59  crossref
    7. ALICE FIALOWSKI, MARTIN SCHLICHENMAIER, “GLOBAL DEFORMATIONS OF THE WITT ALGEBRA OF KRICHEVER–NOVIKOV TYPE”, Commun. Contemp. Math, 05:06 (2003), 921  crossref
    8. MICHEL GOZE, ELISABETH REMM, “VALUED DEFORMATIONS OF ALGEBRAS”, J. Algebra Appl, 03:04 (2004), 345  crossref
    9. Alice Fialowski, Martin Schlichenmaier, “Global Geometric Deformations of Current Algebras as Krichever-Novikov Type Algebras”, Comm Math Phys, 260:3 (2005), 579  crossref  mathscinet  zmath  isi  elib
    10. Alice Fialowski, Marc de Montigny, “Deformations and contractions of Lie algebras”, J Phys A Math Gen, 38:28 (2005), 6335  crossref  mathscinet  zmath  isi  elib
    11. ALICE FIALOWSKI, MICHAEL PENKAVA, “VERSAL DEFORMATIONS OF THREE-DIMENSIONAL Lie ALGEBRAS AS L∞ALGEBRAS”, Commun. Contemp. Math, 07:02 (2005), 145  crossref
    12. Yu. Yu. Kochetkov, “Deformations of the Infinite-Dimensional Lie Algebra $L_3$”, Funct. Anal. Appl., 40:3 (2006), 228–233  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. Abdenacer Makhlouf, “A Comparison of Deformations and Geometric Study of Varieties of Associative Algebras”, Int J Math Math Sci, 2007 (2007), 1  crossref  mathscinet  zmath
    14. Alice Fialowski, Michael Penkava, “Examples of miniversal deformations of infinity algebras”, form, 19:3 (2007), 463  crossref  mathscinet  zmath  isi
    15. ALICE FIALOWSKI, MICHAEL PENKAVA, “DEFORMATIONS OF FOUR-DIMENSIONAL Lie ALGEBRAS”, Commun. Contemp. Math, 09:01 (2007), 41  crossref
    16. Martin Bordemann, Abdenacer Makhlouf, “Formality and Deformations of Universal Enveloping Algebras”, Int J Theor Phys, 47:2 (2008), 311  crossref  mathscinet  zmath  isi
    17. Alice Fialowski, Michael Penkava, “Formal Deformations, Contractions and Moduli Spaces of Lie Algebras”, Int J Theor Phys, 47:2 (2008), 561  crossref  mathscinet  zmath  isi
    18. Alice Fialowski, “Deformations in Mathematics and Physics”, Int J Theor Phys, 47:2 (2008), 333  crossref  mathscinet  zmath  isi
    19. Mabrouk Ben Ammar, Maha Boujelbene, “$\mathfrak{sl}(2)$-Trivial Deformations of $\operatorname{Vect}_{\mathrm{Pol}}(\mathbb R)$-Modules of Symbols”, SIGMA, 4 (2008), 065, 19 pp.  mathnet  crossref  mathscinet  zmath
    20. Faouzi Ammar, Kaouthar Kamoun, “Deforming $\mathcal{K}(1)$ superalgebra modules of symbols”, J Gen Lie Theory Appl, 3:2 (2009), 95  crossref
    21. Alice Fialowski, Michael Penkava, “The Moduli Space of 3-Dimensional Associative Algebras”, Communications in Algebra, 37:10 (2009), 3666  crossref
    22. IMED BASDOURI, MABROUK BEN AMMAR, NIZAR BEN FRAJ, MAHA BOUJELBENE, KAOUTHAR KAMOUN, “COHOMOLOGY OF THE Lie SUPERALGEBRA OF CONTACT VECTOR FIELDS ON �1|1AND DEFORMATIONS OF THE SUPERSPACE OF SYMBOLS”, J. Nonlinear Math. Phys, 16:04 (2009), 373  crossref
    23. Imed Basdouri, Mabrouk Ben Ammar, Béchir Dali, Salem Omri, “Deformation of -modules of symbols”, Journal of Geometry and Physics, 60:3 (2010), 531  crossref
    24. Yunhe Sheng, “On Deformations of Lie Algebroids”, Results. Math, 2011  crossref
    25. Mohamed Elhamdadi, Abdenacer Makhlouf, “Cohomology and Formal Deformations of Alternative Algebras”, J. Gen. Lie Theory Appl, 5 (2011), 1  crossref
    26. Ammar F., Ejbehi Z., Makhlouf A., “Cohomology and Deformations of Hom-Algebras”, J. Lie Theory, 21:4 (2011), 813–836  mathscinet  zmath  isi
    27. Alice Fialowski, “Formal rigidity of the Witt and Virasoro algebra”, J. Math. Phys, 53:7 (2012), 073501  crossref
    28. Basdouri I., Ben Ammar M., “Deformation of and -Modules of Symbols”, Acta Math. Hung., 137:3 (2012), 214–223  crossref  mathscinet  isi
    29. Fialowski A., Magnin L., Mandal A., “About Leibniz Cohomology and Deformations of Lie Algebras”, J. Algebra, 383 (2013), 63–77  crossref  mathscinet  isi
    30. Faouzi Ammar, Abdenacer Makhlouf, Nejib Saadaoui, “Second cohomology of q-deformed Witt superalgebras”, J. Math. Phys, 54:6 (2013), 063507  crossref
    31. Proc. Steklov Inst. Math., 286 (2014), 240–252  mathnet  crossref  crossref  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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