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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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Journal of Mathematical Sciences (New York), 2011, 177:6, 868–877
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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
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\vol 16
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\pages 135--148
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\jour J. Math. Sci.
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http://mi.mathnet.ru/eng/fpm1324 http://mi.mathnet.ru/eng/fpm/v16/i3/p135
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This publication is cited in the following articles:
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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
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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
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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
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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
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A. V. Grishin, “Asymptotics of the Codimensions $c_n$ in the Algebra $F^{(7)}$”, Math. Notes, 104:1 (2018), 22–28
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S. V. Pchelintsev, “Identities of the model algebra of multiplicity 2”, Siberian Math. J., 59:6 (2018), 1105–1124
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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
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