Lie and Jordan products in interchange algebras

  1. Bremner, M. 1
  2. Madariaga, S. 1
  1. 1 University of Saskatchewan
    info

    University of Saskatchewan

    Saskatoon, Canadá

    ROR https://ror.org/010x8gc63

Revista:
Communications in Algebra

ISSN: 0092-7872

Año de publicación: 2016

Volumen: 44

Número: 8

Páginas: 3485-3508

Tipo: Artículo

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DOI: 10.1080/00927872.2015.1085545 SCOPUS: 2-s2.0-84969942269 arXiv: 1408.3069 GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Communications in Algebra

Resumen

We study Lie brackets and Jordan products derived from associative operations ∘,∙ satisfying the interchange identity (w∙x)∘(y∙z)≡(w∘y)∙(x∘z). We use computational linear algebra, based on the representation theory of the symmetric group, to determine all polynomial identities of degree ≤7 relating (i) the two Lie brackets, (ii) one Lie bracket and one Jordan product, and (iii) the two Jordan products. For the Lie-Lie case, there are two new identities in degree 6 and another two in degree 7. For the Lie-Jordan case, there are no new identities in degree ≤6 and a complex set of new identities in degree 7. For the Jordan-Jordan case, there is one new identity in degree 4, two in degree 5, and complex sets of new identities in degrees 6 and 7