Conformal field algebras with quantum symmetry from the theory of superselection sectors

According to the theory of superselection sectors of Doplicher, Haag, and Roberts, field operators which make transitions between different superselection sectors—i.e. different irreducible representations of the observable algebra—are to be constructed by adjoining localized endomorphisms to the algebra of local observables. We find the relevant endomorphisms of the chiral algebra of observables in the minimal conformal model with central chargec=1/2 (Ising model). We show by explicit and elementary construction how they determine a representation of the braid groupB which is associated with a Temperley-Lieb-Jones algebra. We recover fusion rules, and compute the quantum dimensions of the superselection sectors. We exhibit a field algebra which is quantum group covariant and acts in the Hilbert space of physical states. It obeys local braid relations in an appropriate weak sense.     

[2+2]-Photocycloaddition von Cyclohexen an 2-Acetyl-5,5-dimethyl-1,3-cyclohexandion und 3-Acetyl-1,5,5-trimethyl-2,4-pyrrolidindion

Summary Irradiation of solutions of excess cyclohexene and 2-acetyl-5,5-dimethyl-1,3-cyclohexanedione (1), and 3-acetyl-1,5,5-trimethyl-2,4-pyrrolidinedione (4) results mainly in the formation of 1,5-diones2 and5. These originate from intermediate cycloadducts of cyclohexene and theexo-enols of the cyclic 1,3-diketones. The yields decrease with increasing polarity of the solvent. In solution2 and5 are in equilibrium with the cyclic hemiacetales3 and6.