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Fundam. Prikl. Mat., 2010, Volume 16, Issue 3, Pages 135–148 (Mi fpm1324)  

This article is cited in 7 scientific papers (total in 7 papers)

On $T$-spaces and relations in relatively free, Lie nilpotent, associative algebras

A. V. Grishin, L. M. Tsybulya, A. A. Shokola

Moscow State Pedagogical University

Abstract: The purpose of this work is to obtain the commutator relations and Frobenius relations in a relatively free algebra $F^{(l)}$ specified by the identity $[x_1,…,x_l]=0$ over a field of characteristic $p>0$. These relations for $l>3$ are analogous to the relations in the algebra $F^{(3)}$ and are applied to the $T$-spaces in the algebra $F^{(l)}$. In order to study the relations in $F^{(l)}$ in more detail, we construct a model algebra analogous to the Grassmann algebra.

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English version:
Journal of Mathematical Sciences (New York), 2011, 177:6, 868–877

Bibliographic databases:

UDC: 512.552

Citation: A. V. Grishin, L. M. Tsybulya, A. A. Shokola, “On $T$-spaces and relations in relatively free, Lie nilpotent, associative algebras”, Fundam. Prikl. Mat., 16:3 (2010), 135–148; J. Math. Sci., 177:6 (2011), 868–877

Citation in format AMSBIB
\Bibitem{GriTsySho10}
\by A.~V.~Grishin, L.~M.~Tsybulya, A.~A.~Shokola
\paper On $T$-spaces and relations in relatively free, Lie nilpotent, associative algebras
\jour Fundam. Prikl. Mat.
\yr 2010
\vol 16
\issue 3
\pages 135--148
\mathnet{http://mi.mathnet.ru/fpm1324}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2786534}
\elib{http://elibrary.ru/item.asp?id=16350331}
\transl
\jour J. Math. Sci.
\yr 2011
\vol 177
\issue 6
\pages 868--877
\crossref{https://doi.org/10.1007/s10958-011-0515-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80052383498}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Grishin, “On $T$-spaces in a relatively free two-generated Lie nilpotent associative algebra of index $4$”, J. Math. Sci., 191:5 (2013), 686–690  mathnet  crossref
    2. A. V. Grishin, S. V. Pchelintsev, “On centres of relatively free associative algebras with a Lie nilpotency identity”, Sb. Math., 206:11 (2015), 1610–1627  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. A. V. Grishin, S. V. Pchelintsev, “Proper central and core polynomials of relatively free associative algebras with identity of Lie nilpotency of degrees 5 and 6”, Sb. Math., 207:12 (2016), 1674–1692  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. A. V. Grishin, “On the additive structure and asymptotics of codimensions $c_n$ in the algebra $F^{(5)}$”, J. Math. Sci., 233:5 (2018), 666–674  mathnet  crossref  elib
    5. A. V. Grishin, “Asymptotics of the Codimensions $c_n$ in the Algebra $F^{(7)}$”, Math. Notes, 104:1 (2018), 22–28  mathnet  crossref  crossref  isi  elib
    6. S. V. Pchelintsev, “Identities of the model algebra of multiplicity 2”, Siberian Math. J., 59:6 (2018), 1105–1124  mathnet  crossref  crossref  isi
    7. A. V. Grishin, “On the measure of inclusion in relatively free algebras with the identity of Lie nilpotency of degree 3 or 4”, Sb. Math., 210:2 (2019), 234–244  mathnet  crossref  crossref  adsnasa  isi  elib
  • Фундаментальная и прикладная математика
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