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Mat. Sb. (N.S.), 1981, Volume 115(157), Number 1(5), Pages 98–115 (Mi msb2374)  

This article is cited in 24 scientific papers (total in 24 papers)

Representations of the symmetric group and varieties of linear algebras

V. S. Drenski


Abstract: The representation theory of the symmetric group is used to study varieties of linear algebras over a field of characteristic 0. The relatively free algebras and the lattice of subvarieties of the variety of Lie algebras $\mathfrak{AN}_2\cap\mathfrak N_2\mathfrak A$ are described. An example of an almost finitely based variety of linear algebras if constructed. A continuous set of locally finite varieties forming a chain with respect to inclusion is indicated. Information is obtained on the variety of Lie algebras (resp., associative algebras with 1) generated by the second-order matrix algebra. In particular, distributivity of the lattice of subvarieties is proved, and in the Lie case a relatively free algebra is described.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 43:1, 85–101

Bibliographic databases:

UDC: 519.48
MSC: Primary 20B30, 17A60, 17B05; Secondary 16A42
Received: 10.01.1980

Citation: V. S. Drenski, “Representations of the symmetric group and varieties of linear algebras”, Mat. Sb. (N.S.), 115(157):1(5) (1981), 98–115; Math. USSR-Sb., 43:1 (1982), 85–101

Citation in format AMSBIB
\Bibitem{Dre81}
\by V.~S.~Drenski
\paper Representations of the symmetric group and varieties of linear algebras
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 115(157)
\issue 1(5)
\pages 98--115
\mathnet{http://mi.mathnet.ru/msb2374}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=618589}
\zmath{https://zbmath.org/?q=an:0487.17008|0465.17007}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 1
\pages 85--101
\crossref{https://doi.org/10.1070/SM1982v043n01ABEH002411}


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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. S. P. Mishchenko, “The Engel identity and its application”, Math. USSR-Sb., 49:2 (1984), 419–426  mathnet  crossref  mathscinet  zmath
    2. S. P. Mishchenko, “On the Engel problem”, Math. USSR-Sb., 52:1 (1985), 53–62  mathnet  crossref  mathscinet  zmath
    3. Vesselin Drensky, “On the Hilbert series op relatively free algebras”, Communications in Algebra, 12:19 (1984), 2335  crossref
    4. Vesselin Drensky, “Polynomial identities for the Jordan algebra of a symmetric bilinear form”, Journal of Algebra, 108:1 (1987), 66  crossref
    5. Giulia Maria Piacentini Cattaneo, “Alcuni metodi computazionali in algebra”, Seminario Mat e Fis di Milano, 60:1 (1990), 223  crossref  zmath
    6. S. P. Mishchenko, “Growth in varieties of Lie algebras”, Russian Math. Surveys, 45:6 (1990), 27–52  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. S. P. Mishchenko, “On varieties of Lie algebras not containing a three-dimensional simple algebra”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 189–197  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. M. V. Zaicev, “Special Lie algebras”, Russian Math. Surveys, 48:6 (1993), 111–152  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. 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
    10. Drensky V., “Polynomial identity rings - Part A - Combinatorial aspects in PI-rings”, Polynomial Identity Rings, Advanced Courses in Mathematics Crm Barcelona, 2004, 1  isi
    11. S. Mishchenko, A. Valenti, “A Leibniz variety with almost polynomial growth”, Journal of Pure and Applied Algebra, 202:1-3 (2005), 82  crossref
    12. 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
    13. Mishchenko S., Valenti A., “On the growth of varieties of algebras”, Groups, Rings and Group Rings, Contemporary Mathematics, 499, 2009, 229–243  isi
    14. A. Ya. Belov, “The local finite basis property and local representability of varieties of associative rings”, Izv. Math., 74:1 (2010), 1–126  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. Mishchenko S., Valenti A., “Varieties with at most quadratic growth”, Israel Journal of Mathematics, 178:1 (2010), 209–228  crossref  isi
    16. Gordienko A.S., “Graded Polynomial Identities, Group Actions, and Exponential Growth of Lie Algebras”, J. Algebra, 367 (2012), 26–53  crossref  mathscinet  mathscinet  isi
    17. Yu. R. Pestova, “O novykh svoistvakh nekotorykh mnogoobrazii pochti polinomialnogo rosta”, Chebyshevskii sb., 16:2 (2015), 186–207  mathnet  elib
    18. 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
    19. KanelBelov A., Karasik Y., Rowen L., “Computational Aspects of Polynomial Identities: Vol 1, Kemer'S Theorems, 2Nd Edition”, Computational Aspects of Polynomial Identities: Vol 1, Kemer'S Theorems, 2Nd Edition, Monographs and Research Notes in Mathematics, 16, Crc Press-Taylor & Francis Group, 2016, 1–407  mathscinet  isi
    20. S. M. Ratseev, “Chislovye kharakteristiki mnogoobrazii algebr Puassona”, Fundament. i prikl. matem., 21:2 (2016), 217–242  mathnet
    21. Fidelis C., Diniz D., Koshlukov P., “Embeddings For the Jordan Algebra of a Bilinear Form”, Adv. Math., 337 (2018), 294–316  crossref  mathscinet  zmath  isi  scopus
    22. S. P. Mischenko, O. V. Shulezhko, “Mnogoobraziya s drobnym polinomialnym rostom i problema Shpekhta”, Chebyshevskii sb., 19:1 (2018), 176–186  mathnet  crossref  elib
    23. Centrone L. Martino F. Souza Manuela da Silva, “Specht Property For Some Varieties of Jordan Algebras of Almost Polynomial Growth”, J. Algebra, 521 (2019), 137–165  crossref  mathscinet  zmath  isi  scopus
    24. Mishchenko S., Valenti A., “Varieties With At Most Cubic Growth”, J. Algebra, 518 (2019), 321–342  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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