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...

For symplectic Lie algebras sp(2n,C), denote by b and n its Borel subalgebra and maximal nilpotent subalgebra, respectively. We construct a relationship between the abelian ideals of b and the cohomology of n with trivial coefficients. By this relationship, we can enumerate the number of abelian ideals of b with certain dimension via the Poincaré polynomials of Weyl groups of type An−1 and Cn.

We establish branching rules between some Iwahori-Hecke algebra of type B and their subalgebras which are defined as fixed subalgebras by involutions including Goldman involution. The IwahoriHecke algebra of type D is one of such fixed subalgebras. We also obtain branching rules between those fixed subalgebras and their intersection subalgebra. We determine basic sets of irreducible representat...