On maximal non-selfadjoint reflexive algebras associated with a double triangle lattice

We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(L) ∩ Alg(L)^+.Our method can be used to prove similar results in finite-dimensional matrix algebras.As a consequence,we give a new proof to the main theorem by Hou and Zhang(2012).

Structure and frustrated magnetism of the two-dimensional triangular lattice antiferromagnet Na_(2)BaNi(PO_(4))_(2)

A new frustrated triangular lattice antiferromagnet Na_(2)BaNi(PO_(4))_(2) was synthesized by high temperature flux method.The two-dimensional triangular lattice is formed by the Ni^(2+)ions with S=1.Its magnetism is highly anisotropic with the Weiss constants θCW=6.615 K(H||c)and43.979 K(H⊥c).However,no magnetic ordering is present down to 0.3 K,reflecting strong geometric spin frustration.Our heat capacity measurements show substantial residual magnetic entropy existing below 0.3 K at zero field,implying the presence of low energy spin excitations.These results indicate that Na_(2)BaNi(PO_(4))_(2) is a potential spin liquid candidate with spin-1.

φ-Derivations on Strongly Double Triangle Subspace Lattice Algebras

Let D= {{0},/4, L, M, X} be a strongly double triangle subspace lattice on a nonzero complex reflexive Banach space X, which satisfies that one of three sums K ＋ L, L＋M and M ＋ K is closed. It is shown that local C-derivations and C-derivations at zero point on Alg：D are generalized Ф-derivations.

On Strong Kadison–Singer Algebras

We show that many Kadison-Singer algebras are maximal triangular in all algebras containing them although their definition requires the maximality taken in the class of reflexive algebras. Diagonal-trivial maximal non self-adjoint subalgebras of matrix algebras with lower dimensions are classified.