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PI non-equivalence in positive characteristic

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Abstract

The algebras A a,b appeared in the study of the tensor products of verbally prime PI algebras. They are in-between the well known algebras M n (E) and \({M_{a,b}(E)\otimes E}\), see the definitions below. Here E is the Grassmann algebra. The main result of this note consists in showing that the algebras A a,b and M a+b (E) are not PI equivalent in characteristic p > 2.

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References

  1. Alves S.M.: PI (non)equivalence and Gelfand-Kirillov dimension in positive characteristic. Rendiconti del Circolo Matematico di Palermo 58, 109–124 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alves S.M., Koshlukov P.: Polynomial identities of algebras in positive characteristic. J. Algebr. 305, 1149–1165 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Azevedo S.S., Fidelis M., Koshlukov P.: Tensor product theorems in positive characteristic. J. Algebr. 276(2), 836–845 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Azevedo S.S., Fidelis M., Koshlukov P.: Graded identities and PI equivalence of algebras in positive characteristic. Commun. Algebr. 33(4), 1011–1022 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Berele A.: Generic verbally prime algebras and their GK-dimensions. Commun. Algebr. 21(5), 1487–1504 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  6. Di Vincenzo O.M.: On the graded identities of M 1,1(E). Isr. J. Math. 80(3), 323–335 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  7. Di Vincenzo O.M., Nardozza V.: \({\mathbb{Z}_{k+l}\times \mathbb{Z}_2}\)-graded polynomial identities for \({M_{k,l}(E)\otimes E}\). Rend. Sem. Mat. Univ. Padova 108, 27–39 (2002)

    MATH  MathSciNet  Google Scholar 

  8. Di Vincenzo O.M., Nardozza V.: Graded polynomial identities for tensor products by the Grassmann algebra. Commun. Algebr. 31(3), 1453–1474 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Koshlukov P., Azevedo S.S.: Graded identities for T-prime algebras over fields of positive characteristic. Isr. J. Math. 128, 157–176 (2002)

    Article  MATH  Google Scholar 

  10. Regev A.: Tensor products of matrix algebras over the Grassmann algebra. J. Algebr. 133(2), 512–526 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  11. Regev A.: Grassmann algebras over finite fields. Commun. Algebr. 19, 1829–1849 (1991)

    Article  MATH  MathSciNet  Google Scholar 

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  1. DCET, UESC, Rodovia Ilhéus/Itabuna, Km 16, Salobrinho, Ilhéus, Ba, CEP 45662-900, Brazil

    Sérgio Mota Alves

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  1. Sérgio Mota Alves
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Correspondence to Sérgio Mota Alves.

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Alves, S.M. PI non-equivalence in positive characteristic. manuscripta math. 131, 145–147 (2010). https://doi.org/10.1007/s00229-009-0306-z

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  • DOI: https://doi.org/10.1007/s00229-009-0306-z

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