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Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 4, Pages 3–18 (Mi izv689)  

This article is cited in 6 scientific papers (total in 6 papers)

Growth of some varieties of Lie superalgebras

M. V. Zaiceva, S. P. Mishchenkob

a M. V. Lomonosov Moscow State University
b Ulyanovsk State University

Abstract: We study numerical characteristics of varieties of Lie superalgebras and, in particular, the growth of codimensions. An example of an insoluble variety of almost polynomial growth is constructed. We prove that the exponent of this variety is equal to three and calculate the growth exponents for two earlier known soluble varieties.

DOI: https://doi.org/10.4213/im689

Full text: PDF file (516 kB)
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English version:
Izvestiya: Mathematics, 2007, 71:4, 657–672

Bibliographic databases:

UDC: 512.8
MSC: 08B15, 08B99, 17A30, 17A99, 17B01, 17B20, 17B30, 17B40, 17B45, 17B65, 17B70, 17B99, 17C05, 16R10, 16S50, 20C30, 30D20, 16Rxx
Received: 14.11.2005

Citation: M. V. Zaicev, S. P. Mishchenko, “Growth of some varieties of Lie superalgebras”, Izv. RAN. Ser. Mat., 71:4 (2007), 3–18; Izv. Math., 71:4 (2007), 657–672

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. Giambruno A. Zaicev M., “On codimension growth of finite-dimensional Lie superalgebras”, J. Lond. Math. Soc. (2), 85:2 (2012), 534–548  crossref  mathscinet  zmath  isi  scopus
    3. Antonio Giambruno, M.d.a.S.ilva Souza, “Minimal varieties of graded Lie algebras of exponential growth and the special Lie algebra”, Journal of Pure and Applied Algebra, 2013  crossref  mathscinet  isi  scopus
    4. Repovs D., Zaicev M., “On Identities of Infinite Dimensional Lie Superalgebras”, Proc. Amer. Math. Soc., 141:12 (2013), 4139–4153  crossref  mathscinet  zmath  isi  elib  scopus
    5. Mikhail Zaicev, “On existence of PI-exponents of codimension growth”, ERA-MS, 21 (2014), 113  crossref  mathscinet  zmath
    6. Repovs D., Zaicev M., “Graded Identities of Some Simple Lie Superalgebras”, Algebr. Represent. Theory, 17:5 (2014), 1401–1412  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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