Some Infinite-Dimensional Algebras Arising in Spin Systems and in Particle Physics and their Grand Algebra

We indicate similarities in the structure of two types of infinite-dimensional algebras, one introduced 28 years ago in connection with the mass problem of elementary particles and the other seven years ago in connection with spin systems (XY models). We show that these algebras can be considered as representations of a single Grand Algebra, the enveloping algebra of an affine Kac–Moody algebra built on the Poincaré Lie algebra. As an associative and coassociative bialgebra of operators, the latter representation of the grand algebra is a preferred nontrivial deformation of the Ising case bialgebra.     

Silicon-phthalocyanine-cored fullerene dendrimers: synthesis and prolonged charge-separated states with dendrimer generations

Silicon-phthalocyanine-cored fullerodendrimers with up to eight fullerene substituents (SiPc-n C(60); n=2, 4, and 8) have been synthesized. Photophysical properties of newly synthesized SiPc-n C(60) have been investigated by time-resolved fluorescence and transient absorption analysis with pulsed laser light. Laser photolysis measurements suggest the occurrence of a charge-separation process from (1)SiPc* to the C(60) subunits. The nanosecond transient absorption spectra in the near-IR region indicate that the lifetimes of the formed radical ion pairs are prolonged on the order of SiPc-8 C(60)>SiPc-4 C(60)>SiPc-2 C(60), which may be related to the electron migration among the C(60) subunits. The usefulness of SiPc-n C(60) as light-harvesting systems, evaluated as a ratio of the rates of charge recombination to those of charge separation, increases markedly with the dendrimer generation.