Now showing items 1-6 of 6

    • An algorithm for associative bilinear forms 

      Arenas, Manuel (2009)
      We establish the equivalence between the problem of existence of associative bilinear forms and the problem of solvability in commutative power-associative finite-dimensional nil-algebras. We use the tensor product to find ...
    • On nilpotency of generalized almost-jordan right-nilalgebras 

      Arenas, Manuel; Labra, Alicia (World Scientific Publishing Co. Pte Ltd, 2008)
      We study the variety of algebras A over a field of characteristic ≠ 2, 3, 5 satisfying the identities xy=yx and β ((xx)y)x-((yx)x)x + γ ((xx)x)y-((yx)x)x=0, where β, γ are scalars. We do not assume power-associativity. We ...
    • On optimal embeddings and trees 

      Arenas, Manuel; Arenas Carmona, Luis; Contreras, Jaime (Academic Press Inc., 2018)
      © 2018 Elsevier Inc. We apply the theory of Bruhat–Tits trees to the study of optimal embeddings from orders of rank two and three to quaternion algebras. Specifically, we determine how many conjugacy classes of global ...
    • On speciality of binary-Lie algebras 

      Arenas, Manuel; Shestakov, Ivan (World Scientific Publishing Co. Pte Ltd, 2011)
      In the present work, binary-Lie, assocyclic, and binary (-1,1) algebras are studied. We prove that, for every assocyclic algebra A, the algebra A - is binary-Lie. We find a simple non-Malcev binary-Lie superalgebra T that ...
    • The Wedderburn principal theorem for generalized almost-Jordan algebras 

      Arenas, Manuel (2007)
      We study commutative algebras A over fields of characteristic ≠2, 3 which satisfy the identity β{x(y(xx)) - x(x(xy))} + γ{y(x(xx)) - x(x(xy))} = 0. We do not assume power-associativity. We find the Peirce decomposition of ...
    • Universal Poisson Envelope for Binary-Lie Algebras 

      Arenas, Manuel; Arenas Carmona, Luis (2013)
      In this article the universal Poisson enveloping algebra for a binary-Lie algebra is constructed. Taking a basis B{double-struck} of a binary-Lie algebra B, we consider the symmetric algebra S(B) of polynomials in the ...