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3 results

  • Polynomial Lie Subalgebras of the Infinite Matrix Lie Algebra

  • Liang Chen
  • Journal:
    Canadian Journal of Mathematics / Volume 48 / Issue 2 / 01 April 1996
    Published online by Cambridge University Press:
    20 November 2018, pp. 274-287
    Print publication:
    01 April 1996
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  • We construct two classes of Lie subalgebras of the infinite matrix Lie algebra 𝔤𝔩∞(ℂ) and prove that they are all simple Lie algebras.

  • Indecomposable Positive Maps in Matrix Algebras

  • Kôtarô Tanahashi, Jun Tomiyama
  • Journal:
    Canadian Mathematical Bulletin / Volume 31 / Issue 3 / 01 September 1988
    Published online by Cambridge University Press:
    20 November 2018, pp. 308-317
    Print publication:
    01 September 1988
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  • We prove that Choi's map in M3 cannot be written as the sum of a 2-positive map and a 2-copositive map. We also provide other examples of positive maps in Mn which cannot be written as the sum of an n-positive map and a 2-copositive map.

  • Solvable Groups of Unipotent Elements in a Ring

  • Abraham A. Klein
  • Journal:
    Canadian Mathematical Bulletin / Volume 25 / Issue 2 / 01 June 1982
    Published online by Cambridge University Press:
    20 November 2018, pp. 187-190
    Print publication:
    01 June 1982
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  • Let R be a ring with 1 whose nil subrings are nilpotent modulo the sum of nilpotent ideals. It is proved that if G is a locally solvable group of unipotent elements in R, then the subring generated by {g −1 g ∈ G} is nil. This result implies a result of Sizer showing that a solvable group of unipotent matrices over a skew field can be simultaneously triangularized.