We introduce a new notion of a sufficient subalgebra for quantum states: a subalgebra is 2sufficient for a pair of states {ρ0, ρ1} if it contains all Bayes optimal tests of ρ0 against ρ1. In classical statistics, this corresponds to the usual definition of sufficiency. We show this correspondence in the quantum setting for some special cases. Furthermore, we show that sufficiency is equivalent ...

Abstract. In this paper we introduce doubly symmetric functions, arising from the equivalence of particular linear combinations of Schur functions and hook Schur functions. We study algebraic and combinatorial aspects of doubly symmetric functions, in particular as they form a subalgebra of the algebra of symmetric functions. This subalgebra is generated by the odd power sum symmetric functions...

We inquire further into the properties on fuzzy closed ideals. We give a characterization of a fuzzy closed ideal using its level set, and establish some conditions for a fuzzy set to be a fuzzy closed ideal. We describe the fuzzy closed ideal generated by a fuzzy set, and give a characterization of a finite-valued fuzzy closed ideal. Using a t-norm T , we introduce the notion of (imaginable) T...

Perhaps the most celebrated topological completeness result in modal logic is the McKinseyTarski theorem that if we interpret modal diamond as topological closure, then S4 is complete for the real line or indeed any dense-in-itself separable metrizable space [10]. This result was proved before relational semantics for modal logic was introduced. In the last 15 years, utilizing relational semant...

We prove a spectral theorem for bimodules in the context of graph C∗-algebras. A bimodule over a suitable abelian algebra is determined by its spectrum (i.e., its groupoid partial order) iff it is generated by the Cuntz– Krieger partial isometries which it contains iff it is invariant under the gauge automorphisms. We study 1-cocycles on the Cuntz–Krieger groupoid associated with a graph C∗-alg...

We discuss (extended) super Schrödinger algebras obtained as subalgebras of the superconformal algebra psu(2,2|4). The Schrödinger algebra with two spatial dimensions can be embedded into so(4,2). In the superconformal case the embedded algebra may be enhanced to the so-called super Schrödinger algebra. In fact, we find an extended super Schrödinger subalgebra of psu(2,2|4). It contains 24 supe...

We discuss (extended) super Schrödinger algebras which are subalgebras of the superconformal algebra psu(2,2|4). The Schrödinger algebra with two spatial dimensions can be embedded into so(4,2). In the superconformal case the embedded algebra may be enhanced to the so-called super Schrödinger algebra. In fact, we find an extended super Schrödinger subalgebra of psu(2,2|4). It contains, as well ...

A closed subalgebra of a Banach algebra is called maximal if it is not contained in any larger proper closed subalgebra. Let G be a discrete abelian topological group and L its group-algebra, i.e. L is the Banach algebra of functions/on G with E*e<J |/(X)| < °° and multiplication defined as convolution. What are the maximal subalgebras of L? The complete answer is not known even when G is the g...

Division algebras D generated by some finitely generated nilpotent subgroup G of the multiplicative group D* of D are studied and the question to what extent G is determined by D is considered. Trivial examples show that D does not determine G up to isomorphism. However, it is proved that if F denotes the center of D, then the F-subalgebra of D generated by G is in fact determined up to isomorp...

Systems of second-order ordinary differential equations admitting a Lagrangian formulation are deformed requiring that the extended Lagrangian preserves a fixed subalgebra of Noether symmetries of the original system. For the case of the simple Lie algebra sl(2,R), this provides non-linear systems with two independent constants of the motion quadratic in the velocities. In the case of scalar di...