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

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

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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