Results in Mathematics

, Volume 35, Issue 1–2, pp 32–43 | Cite as

Shape identities in train algebras of rank 3

Article
  • 21 Downloads

Abstract

Shape identities are certain multilinear nonassociative polynomials. In this paper we derive some properties of train algebras of rank 3 which satisfy some shape identity of degree at most 5.

En]Keywords

Baric algebras Shape identities Train algebras 

1991 Mathematics Subject Classification

17D92 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Costa, R.: Principal train algebras of rank 3 and dimension ≤ 5, Proc. Edinb. Math. Soc. 33 (1990), 61–70.MATHCrossRefGoogle Scholar
  2. [2]
    Costa, R.: On train algebras of rank 3, Linear Algebra and its Appl. 148 (1991), 1–12.MATHCrossRefGoogle Scholar
  3. [3]
    Costa, R.: Shape identities in Genetic algebras, Linear Algebra Appl., 214, 119–131 (1995).MathSciNetCrossRefGoogle Scholar
  4. [4]
    Costa, R. and Baeza-Vega, R.: Shape identities in Genetic algebras IIGoogle Scholar
  5. [5]
    Etherington, I.M.H.: Genetic Algebras, Proc. Roy. Soc. Edinb. 59, 242–258 (1939).Google Scholar
  6. [6]
    Etherington, I.M.H.: Commutative train algebras of ranks 2 and 3, J. London Math. Soc. 15, 136–149 (1940). Corrigendum ibid 20, 238 (1945).MathSciNetGoogle Scholar
  7. [7]
    Guzzo Jr, H.: Embedding nil algebras in train algebras, Proc. Edinb. Math. Soc. 37, 463–470 (1994).CrossRefGoogle Scholar
  8. [8]
    Guzzo Jr, H. and Vicente, P.: Train algebras of rank n which are Bernstein or Power-Associative algebras, Nova Journal of Mathematics, Game Theory, and Algebra (to appear).Google Scholar
  9. [9]
    Guzzo Jr, H. and Vicente, P.: Some properties of commutative train algebras of rank 3, submitted to Comm. in Algebra.Google Scholar
  10. [10]
    Lyubich, Yu. I.: Mathematical Structures in Population Genetic (Biomathematics 22, Springer, Berlin-Heidelberg-New York1992).Google Scholar
  11. [11]
    Osborn, J.M.: Varieties of algebras, Adv. in Math., 8, 163–369 (1972).CrossRefGoogle Scholar
  12. [12]
    Wörz, A.: Algebras in Genetic (Lecture Notes in Biomathematics 36, Springer, Berlin-Heidelberg-New York 1980).Google Scholar

Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  1. 1.Universidade de São Paulo Instituto de Matemática e EstatísticaSão Paulo —Brazil
  2. 2.Departamento de MatemáticasUniversidad de León Campus de VegazanaLeón —Spain

Personalised recommendations