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Mat. Sb., 2009, Volume 200, Number 9, Pages 41–80 (Mi msb6374)  

This article is cited in 9 scientific papers (total in 9 papers)

On the multiplicative and $T$-space structure of the 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 unity corresponding to the identity $[[x_1,x_2],x_3]=0$ over an infinite field of characteristic $p>0$. One of the basic results is the decomposition of quotient $T$-spaces connected with $F^{(3)}$ into a direct sum of simple components. Also, the $T$-spaces under consideration are commutative subalgebras of $F^{(3)}$; thus, the structure of $F^{(3)}$ and its subalgebras is described as modules over these commutative subalgebras. Finally, we consider the specifics of the case $p=2$.
Bibliography: 15 titles.

Keywords: $T$-space, $T$-ideal, $n$-word, canonical basis, relatively free Grassmann algebra.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm6374

Full text: PDF file (731 kB)
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English version:
Sbornik: Mathematics, 2009, 200:9, 1299–1338

Bibliographic databases:

UDC: 512.552
MSC: 16R10
Received: 10.06.2008 and 13.04.2009

Citation: A. V. Grishin, L. M. Tsybulya, “On the multiplicative and $T$-space structure of the relatively free Grassmann algebra”, Mat. Sb., 200:9 (2009), 41–80; Sb. Math., 200:9 (2009), 1299–1338

Citation in format AMSBIB
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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, L. M. Tsybulya, “On the structure of a relatively free Grassmann algebra”, J. Math. Sci., 171:2 (2010), 149–212  mathnet  crossref  mathscinet  elib
    2. A. V. Grishin, L. M. Tsybulya, A. A. Shokola, “On $T$-spaces and relations in relatively free, Lie nilpotent, associative algebras”, J. Math. Sci., 177:6 (2011), 868–877  mathnet  crossref  mathscinet  elib
    3. 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
    4. Gonçalves D.J., Krasilnikov A., Sviridova I., “Limit $T$-subspaces and the central polynomials in $n$ variables of the Grassmann algebra”, J. Algebra, 371 (2012), 156–174  crossref  mathscinet  zmath  isi  scopus
    5. 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
    6. D. J. Gonçalves, A. Krasilnikov, I. Sviridova, “Limit $T$-subalgebras in free associative algebras”, J. Algebra, 412 (2014), 264–280  crossref  mathscinet  zmath  isi  scopus
    7. G. Deryabina, A. Krasilnikov, “The subalgebra of graded central polynomials of an associative algebra”, J. Algebra, 425 (2015), 313–323  crossref  mathscinet  zmath  isi  elib  scopus
    8. 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
    9. 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
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