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Sibirsk. Mat. Zh., 2018, Volume 59, Number 6, Pages 1389–1411 (Mi smj3052)  

Identities of the model algebra of multiplicity 2

S. V. Pchelintsevab

a Financial University Under the Government of the Russian Federation, Moscow, Russia
b Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We construct an additive basis of the free algebra of the variety generated by the model algebra of multiplicity 2 over an infinite field of characteristic not 2 and 3. Using the basis we remove a restriction on the characteristic in the theorem on identities of the model algebra (previously the same was proved in the case of characteristic 0). In particular, we prove that the kernel of the relatively free Lie-nilpotent algebra of index 5 coincides with the ideal of identities of the model algebra of multiplicity 2.

Keywords: free algebra, proper polynomial, identity of Lie-nilpotency, additive basis, identities of a model algebra.

Funding Agency Grant Number
Russian Science Foundation 14-21-00065
The author was supported by the Russian Science Foundation (Grant 14-21-00065).


DOI: https://doi.org/10.17377/smzh.2018.59.614

Full text: PDF file (387 kB)
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English version:
Siberian Mathematical Journal, 2018, 59:6, 1105–1124

Bibliographic databases:

UDC: 512.552.4+512.572
Received: 30.01.2018

Citation: S. V. Pchelintsev, “Identities of the model algebra of multiplicity 2”, Sibirsk. Mat. Zh., 59:6 (2018), 1389–1411; Siberian Math. J., 59:6 (2018), 1105–1124

Citation in format AMSBIB
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\paper Identities of the model algebra of multiplicity~2
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 6
\pages 1389--1411
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\crossref{https://doi.org/10.17377/smzh.2018.59.614}
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\transl
\jour Siberian Math. J.
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\vol 59
\issue 6
\pages 1105--1124
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