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Uspekhi Mat. Nauk, 1990, Volume 45, Issue 6(276), Pages 25–45 (Mi umn4805)  

This article is cited in 37 scientific papers (total in 37 papers)

Growth in varieties of Lie algebras

S. P. Mishchenko

Ulyanovsk State University

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English version:
Russian Mathematical Surveys, 1990, 45:6, 27–52

Bibliographic databases:

UDC: 519.4
MSC: 17Bxx, 20C30, 20B30
Received: 18.10.1988

Citation: S. P. Mishchenko, “Growth in varieties of Lie algebras”, Uspekhi Mat. Nauk, 45:6(276) (1990), 25–45; Russian Math. Surveys, 45:6 (1990), 27–52

Citation in format AMSBIB
\by S.~P.~Mishchenko
\paper Growth in varieties of Lie algebras
\jour Uspekhi Mat. Nauk
\yr 1990
\vol 45
\issue 6(276)
\pages 25--45
\jour Russian Math. Surveys
\yr 1990
\vol 45
\issue 6
\pages 27--52

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    This publication is cited in the following articles:
    1. M. V. Zaicev, “Special Lie algebras”, Russian Math. Surveys, 48:6 (1993), 111–152  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. M. V. Zaicev, “The base rank of varieties of Lie algebras”, Russian Acad. Sci. Sb. Math., 80:1 (1995), 15–31  mathnet  crossref  mathscinet  zmath  isi
    3. M. V. Zaicev, “Standard identity and Capelli identities in Lie algebras”, Russian Math. Surveys, 49:2 (1994), 186–187  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. M. V. Zaicev, “Skew-symmetric identities in special Lie algebras”, Sb. Math., 186:1 (1995), 65–77  mathnet  crossref  mathscinet  zmath  isi
    5. V. M. Petrogradskii, “O tipakh sverkheksponentsialnogo rosta tozhdestv v PI-algebrakh Li”, Fundament. i prikl. matem., 1:4 (1995), 989–1007  mathnet  mathscinet  zmath
    6. S. P. Mishchenko, “Lower bound on the dimensions or irreducible representations of symmetric groups and on the exponents of varieties of Lie algebras”, Sb. Math., 187:1 (1996), 81–92  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. V. M. Petrogradsky, “Growth of polynilpotent varieties of Lie algebras and rapidly growing entire functions”, Sb. Math., 188:6 (1997), 913–931  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. M. V. Zaicev, “Varieties of affine Kac–Moody algebras”, Math. Notes, 62:1 (1997), 80–86  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. M. V. Zaicev, S. P. Mishchenko, “Varieties of Lie superalgebras of polynomial growth”, Russian Math. Surveys, 52:2 (1997), 432–433  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    10. M. V. Zaicev, S. P. Mishchenko, “A criterion for polynomial growth of varieties of Lie superalgebras”, Izv. Math., 62:5 (1998), 953–967  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. S. P. Mishchenko, “A sufficient condition for the nilpotence of the commutant of a Lie algebra”, Russian Math. (Iz. VUZ), 42:8 (1998), 41–45  mathnet  mathscinet  zmath  elib
    12. V. M. Petrogradsky, “On numerical characteristics of subvarieties for three varieties of Lie algebras”, Sb. Math., 190:6 (1999), 887–902  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. Yuri Bahturin, Sergei Mishchenko, Amitai Regev, “On the lee and associative codimensions growth”, Communications in Algebra, 27:10 (1999), 4901  crossref
    14. Giambruno, A, “Simple and semisimple Lie algebras and codimension growth”, Transactions of the American Mathematical Society, 352:4 (2000), 1935  crossref  mathscinet  zmath  isi  elib
    15. S. Mishchenko, A. Valenti, “A Leibniz variety with almost polynomial growth”, Journal of Pure and Applied Algebra, 202:1-3 (2005), 82  crossref
    16. S. P. Mishchenko, O. I. Cherevatenko, “Necessary and sufficient conditions for a variety of Leibniz algebras to have polynomial growth”, J. Math. Sci., 152:2 (2008), 282–287  mathnet  crossref  mathscinet  zmath  elib  elib
    17. S. N. Tronin, “Operads and varieties of algebras defined by polylinear identities”, Siberian Math. J., 47:3 (2006), 555–573  mathnet  crossref  mathscinet  zmath  isi  elib
    18. M. V. Zaitsev, S. P. Mishchenko, “Identities for Lie superalgebras with a nilpotent commutator subalgebra”, Algebra and Logic, 47:5 (2008), 348–364  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    19. Giambruno A., Zaicev M., “Proper identities, Lie identities and exponential codimension growth”, J Algebra, 320:5 (2008), 1933–1962  crossref  isi
    20. Giambruno A., Mishchenko S., Zaicev M., “Codimensions of algebras and growth functions”, Adv Math, 217:3 (2008), 1027–1052  crossref  isi
    21. Mishchenko S., Valenti A., “On the growth of varieties of algebras”, Groups, Rings and Group Rings, Contemporary Mathematics, 499, 2009, 229–243  isi
    22. Giambruno A., Zaicev M., “Codimension Growth of Special Simple Jordan Algebras”, Trans Amer Math Soc, 362:6 (2010), 3107–3123  isi
    23. Giambruno A., Zaicev M., “On Codimension Growth of Finite-Dimensional Lie Superalgebras”, J. Lond. Math. Soc.-Second Ser., 85:Part 2 (2012), 534–548  crossref  isi
    24. S. P. Mishchenko, Y. R. Fyathutdinova, “New properties of the Lie algebra variety $\mathbf N_2\mathbf A$”, J. Math. Sci., 197:4 (2014), 558–564  mathnet  crossref
    25. Repovs D., Zaicev M., “On the Codimension Growth of Almost Nilpotent Lie Algebras”, Isr. J. Math., 194:1 (2013), 137–150  crossref  isi
    26. Repovs D., Zaicev M., “On Identities of Infinite Dimensional Lie Superalgebras”, Proc. Amer. Math. Soc., 141:12 (2013), 4139–4153  isi
    27. Alexei Belov-Kanel, Antonio Giambruno, L.H.alle Rowen, Uzi Vishne, “Zariski Closed Algebras in Varieties of Universal Algebra”, Algebr Represent Theor, 2014  crossref
    28. S. P. Mischenko, Yu. R. Pestova, “Bazis polilineinoi chasti mnogoobraziya algebr Leibnitsa $\widetilde{\mathrm{V}}_1$”, Vestn. SamGU. Estestvennonauchn. ser., 2014, no. 3(114), 76–82  mathnet
    29. Mikhail Zaicev, “On existence of PI-exponents of codimension growth”, ERA-MS, 21 (2014), 113  crossref
    30. O. V. Shulezhko, “O pochti nilpotentnykh mnogoobraziyakh v razlichnykh klassakh lineinykh algebr”, Chebyshevskii sb., 16:1 (2015), 67–88  mathnet  elib
    31. S. M. Ratseev, “Lie algebras with extremal properties”, Siberian Math. J., 56:2 (2015), 358–366  mathnet  crossref  mathscinet  isi  elib  elib
    32. Yu. R. Pestova, “O novykh svoistvakh nekotorykh mnogoobrazii pochti polinomialnogo rosta”, Chebyshevskii sb., 16:2 (2015), 186–207  mathnet  elib
    33. M. V. Zaicev, D. Repovš, “Exponential growth of codimensions of identities of algebras with unity”, Sb. Math., 206:10 (2015), 1440–1462  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    34. Yu. R. Pestova, “Colength of the variety generated by a three-dimensional simple Lie algebra”, Moscow University Mathematics Bulletin, 70:3 (2015), 144–147  mathnet  crossref  mathscinet  isi
    35. M. V. Zaicev, “Growth of codimensions of metabelian algebras”, Moscow University Mathematics Bulletin, 72:6 (2017), 233–237  mathnet  crossref  mathscinet  isi
    36. M. V. Zaicev, D. D. Repovš, “Combinatorics on binary words and codimensions of identities in left nilpotent algebras”, Algebra and Logic, 58:1 (2019), 23–35  mathnet  crossref  crossref  isi
    37. M. V. Zaitsev, S. P. Mischenko, “Posledovatelnosti korazmernostei tozhdestv i ikh asimptoticheskoe povedenie”, Fundament. i prikl. matem., 22:4 (2019), 115–127  mathnet
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