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Fundam. Prikl. Mat., 1995, Volume 1, Issue 4, Pages 989–1007 (Mi fpm118)  

This article is cited in 17 scientific papers (total in 17 papers)

On types of overexponential growth in Lie PI-algebras

V. M. Petrogradsky

Ul'yanovsk Branch of M. V. Lomonosov Moscow State University

Abstract: The growth function of identities $c_n(\mathcal{V})$ for varieties of Lie algebras is studied; where $c_n(\mathcal{V})$ is the dimension of a linear span of multilinear words in $n$ distinct letters in a free algebra $F(\mathcal{V},X)$ of the variety $\mathcal{V}$. The main results are as follows: the description of types of overexponential growth is suggested; the growth of identities for polynilpotent varieties is found. A complexity function $\mathcal{C}(\mathcal{V},z)$ is used; it corresponds to any nontrivial variety of Lie algebras $\mathcal{V}$ and is an entire function of a complex variable.

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UDC: 512.554.33
Received: 01.03.1995

Citation: V. M. Petrogradsky, “On types of overexponential growth in Lie PI-algebras”, Fundam. Prikl. Mat., 1:4 (1995), 989–1007

Citation in format AMSBIB
\by V.~M.~Petrogradsky
\paper On types of overexponential growth in Lie PI-algebras
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 4
\pages 989--1007

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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. 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
    4. Petrogradsky V.M., “Exponential generating functions and complexity of Lie varieties”, Israel Journal of Mathematics, 113 (1999), 323–339  crossref  mathscinet  zmath  isi
    5. Petrogradsky V.M., “Growth of finitely generated polynilpotent Lie algebras and groups, generalized partitions, and functions analytic in the unit circle”, International Journal of Algebra and Computation, 9:2 (1999), 179–212  crossref  mathscinet  zmath  isi
    6. Mishchenko S.P., Petrogradsky V.M., “Exponents of varieties of Lie algebras with a nilpotent commutator subalgebra”, Communications in Algebra, 27:5 (1999), 2223–2230  crossref  mathscinet  zmath  isi
    7. V. M. Petrogradsky, “On the Complexity Functions for $T$-Ideals of Associative Algebras”, Math. Notes, 68:6 (2000), 751–759  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Petrogradsky V.M., “On growth of Lie algebras, generalized partitions, and analytic functions”, Discrete Mathematics, 217:1–3 (2000), 337–351  crossref  mathscinet  zmath  isi
    9. M. V. Zaicev, “Integrality of exponents of codimension growth of finite-dimensional Lie algebras”, Izv. Math., 66:3 (2002), 463–487  mathnet  crossref  crossref  mathscinet  zmath  elib
    10. Drensky V., “Polynomial identity rings - Part A - Combinatorial aspects in PI-rings”, Polynomial Identity Rings, Advanced Courses in Mathematics CRM Barcelona, 2004, 1  mathscinet  zmath  isi
    11. M. V. Zaicev, S. P. Mishchenko, “Growth of some varieties of Lie superalgebras”, Izv. Math., 71:4 (2007), 657–672  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    12. 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
    13. Giambruno A., Shestakov I., Zaicev M., “Finite-dimensional non-associative algebras and codimension growth”, Adv in Appl Math, 47:1 (2011), 125–139  crossref  mathscinet  zmath  isi
    14. Giambruno A., Zaicev M., “On codimension growth of finite-dimensional Lie superalgebras”, J London Math Soc (2), 85:2 (2012), 534–548  crossref  mathscinet  zmath  isi
    15. S. M. Ratseev, “On minimal Leibniz algebras with nilpotent commutator subalgebra”, St. Petersburg Math. J., 27:1 (2016), 125–136  mathnet  crossref  mathscinet  isi  elib
    16. S. M. Ratseev, “Complexity Functions of Varieties of Leibniz Algebras with Nilpotent Commutator Subalgebra”, Math. Notes, 98:3 (2015), 525–528  mathnet  crossref  crossref  mathscinet  isi  elib
    17. S. M. Ratseev, O. I. Cherevatenko, “Korazmernosti mnogoobrazii algebr Puassona s lievo nilpotentnymi kommutantami”, Tr. IMM UrO RAN, 22, no. 1, 2016, 241–244  mathnet  mathscinet  elib
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