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Codimension Growth of Algebras with Adjoint Unit

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Abstract

In this paper, numerical characteristics of identities of finite-dimensional nonassociative algebras are studied. Main attention is paid to the question on the change of the PI-exponent after adjoining an external unit element. We construct an example of a four-dimensional simple algebra such that its PI-exponent increases by one after adjoining an external unit element.

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Correspondence to O. E. Bezushchak.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 3, pp. 11–26, 2013.

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Bezushchak, O.E., Beljaev, A.A. & Zaicev, M.V. Codimension Growth of Algebras with Adjoint Unit. J Math Sci 206, 462–473 (2015). https://doi.org/10.1007/s10958-015-2325-5

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Keywords

  • Associative Algebra
  • Young Diagram
  • Group Ring
  • Irreducible Character
  • Polynomial Identity