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Siberian Mathematical Journal

, Volume 59, Issue 6, pp 1105–1124 | Cite as

Identities of the Model Algebra of Multiplicity 2

  • S. V. Pchelintsev
Article
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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 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Financial University Under the Government of the Russian FederationMoscowRussia
  2. 2.Sobolev Institute of MathematicsNovosibirskRussia

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