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The central polynomials for the Grassmann algebra

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Abstract

In this paper we describe the central polynomials for the infinite-dimensional unitary Grassmann algebra G over an infinite field F of characteristic ≠ 2. We exhibit a set of polynomials that generates the vector space C(G) of the central polynomials of G as a T-space. Using a deep result of Shchigolev we prove that if charF = p > 2 then the T-space C(G) is not finitely generated. Moreover, over such a field F, C(G) is a limit T-space, that is, C(G) is not a finitely generated T-space but every larger T-space W ≩ C(G) is. We obtain similar results for the infinite-dimensional nonunitary Grassmann algebra H as well.

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Authors and Affiliations

  1. UAME/CCT, UFCG, P.O.Box 10044, 58109-970, Campina Grande, PB, Brazil

    Antônio Pereira Brandão Jr.

  2. IMECC, UNICAMP, P.O.Box 6065, 13083-970, Campinas, SP, Brazil

    Plamen Koshlukov

  3. Departamento de Matemática, Universidade de Brasília, 70910-900, Brasília, DF, Brazil

    Alexei Krasilnikov

  4. Departamento de Matemática, Universidade Federal de Goiás, Campus de Catalão, 75705-220, Catalão, GO, Brazil

    Élida Alves da Silva

Authors
  1. Antônio Pereira Brandão Jr.
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  2. Plamen Koshlukov
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  3. Alexei Krasilnikov
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  4. Élida Alves da Silva
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Correspondence to Antônio Pereira Brandão Jr..

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Partially supported by CNPq

Partially supported by CNPq and by FAPESP

Partially supported by CNPq, FAPDF and FINATEC

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Brandão, A.P., Koshlukov, P., Krasilnikov, A. et al. The central polynomials for the Grassmann algebra. Isr. J. Math. 179, 127–144 (2010). https://doi.org/10.1007/s11856-010-0074-1

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