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Fundam. Prikl. Mat., 2009, Volume 15, Issue 8, Pages 3–93 (Mi fpm1282)  

This article is cited in 4 scientific papers (total in 4 papers)

On the structure of a relatively free Grassmann algebra

A. V. Grishin, L. M. Tsybulya

Moscow State Pedagogical University

Abstract: We investigate the multiplicative and $T$-space structure of the relatively free algebra $F^{(3)}$ with a unity corresponding to the identity $[[x_1,x_2],x_3]=0$ over an infinite field of characteristic $p>0$. The highest emphasis is placed on unitary closed $T$-spaces over a field of characteristic $p>2$. We construct a diagram containing all basic $T$-spaces of the algebra $F^{(3)}$, which form infinite chains of the inclusions. One of the main results is the decomposition of quotient $T$-spaces connected with $F^{(3)}$ into a direct sum of simple components. Also, the studied $T$-spaces are commutative subalgebras of $F^{(3)}$; thus, the structure of $F^{(3)}$ and its subalgebras can be described as modules over these commutative algebras. Separately, we consider the specifics of the case $p=2$. In Appendix, we study nonunitary closed $T$-spaces and the case of a field of zero characteristic.

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English version:
Journal of Mathematical Sciences (New York), 2010, 171:2, 149–212

Bibliographic databases:

UDC: 512.552

Citation: A. V. Grishin, L. M. Tsybulya, “On the structure of a relatively free Grassmann algebra”, Fundam. Prikl. Mat., 15:8 (2009), 3–93; J. Math. Sci., 171:2 (2010), 149–212

Citation in format AMSBIB
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\by A.~V.~Grishin, L.~M.~Tsybulya
\paper On the structure of a~relatively free Grassmann algebra
\jour Fundam. Prikl. Mat.
\yr 2009
\vol 15
\issue 8
\pages 3--93
\mathnet{http://mi.mathnet.ru/fpm1282}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2745014}
\elib{http://elibrary.ru/item.asp?id=15340724}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 171
\issue 2
\pages 149--212
\crossref{https://doi.org/10.1007/s10958-010-0131-7}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78349313679}


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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. A. V. Grishin, “On the Center of a Relatively Free Lie-Nilpotent Algebra of Index $4$”, Math. Notes, 91:1 (2012), 139–140  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. 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
    3. 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
    4. 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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