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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Acta applicandae mathematicae 18 (1990), S. 59-84 
    ISSN: 1572-9036
    Schlagwort(e): 22E65 ; 22E70 ; Highest weight modules ; CCR algebras ; representation theory
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The results of Kashiwara and Vergne on the decomposition of the tensor products of the ‘Segal-Shale-Weil representation’ are extended to the infinite dimensional case and give all unitary lowest weight representations. Our methods are basically algebraic. When restricted to the finite dimensional case, they yield a new proof.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    ISSN: 0018-019X
    Schlagwort(e): Chemistry ; Organic Chemistry
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: A First Example of a Porphyrinoid Fulvalene: Synthesis, Structure, ESR and Electrochemical InvestigationsThe macrocyclic tetraepoxy-1H-[21]annulen-1-one 4 can by synthesized by the cyclizing Wittig reaction of 5,5′-carbonylbis[furan-2-carboxaldehyde] (11) and the bisphosphonium salt 12, obtained from 2,2′-bifuran-5,5′-dicarboxaldehyde (13). According to an X-ray structure analysis, the annulenone 4 is not planar in the crystal; the 1H-NMR spectra of 4 reveal an averaged planarity with respect to the NMR timescale. The McMurry reaction of 4 yields fulvalene 3 in 43% yield as the most expanded fulvalene hithertoo known. The X-ray structure analyses of 3 surprising establishes a ‘syn’-orientation of the two rings with respect to the central C=C bond, thus forming a basket-like molecule. The 1H-NMR spectrum confirms the averaged planarity of both macrocycles in 3. CV and spectroelectrochemical measurements of 3 suggest a reversible two-electron reduction producing dianion 15 with two aromatic, anionic 5a,15a-didehydro-10H-21,22,23,24-tetraoxa-5a,15a-dihomocorrole (= tetraoxa[22]porphyrin(2.1.2.0)) ring systems containing 22π electrons each. The formation of 15 can also be achieved chemically by reaction of 3 with metallic potassium. The dication 16 of 3 may be antiaromatic, but the exact electronic structure is dubious. ESR and ENDOR investigations on the radical cation and the radical anion of 3 indicate that the free electron is delocalized in the entire molecule.
    Zusätzliches Material: 14 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    ISSN: 0018-019X
    Schlagwort(e): Chemistry ; Organic Chemistry
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: Extremely Expanded Tetrathiafulvalenes with Polyene Spacers. Carotinoid Tetrathiafulvalenes. Polymethin-Tetracyanotetrathiafulvalene Radical Cations, a New Class of ViolenesThe synthesis of extended tetrathiafulvalenes 11 with di-, tetra-, hexa-, octa-, deca- and dodecamethine spacers is described by a PPh3-induced Wittig-reaction-like condensation of the corresponding polyenedials 10 with 2-thio-1,3-dithiole-4,5-dicarbonitrile (9). By the same procedure, the dimethyloctamethine- and the tetramethyl-hexadecamethine-tetrathiafulvalenes 14 and 15, respectively, were obtained. The extended tetrathiafulvalenes represent multistep vinylogous redox systems of the ‘violene type’. They can be oxidized to give the cyanine-like radical cations, e.g. 11sem, 14sem, and 15sem, and the dications, e.g. 11ox, 14ox, and 15ox; their UV/VIS/NIR spectra are reported. The crystal and molecular structure of (all-E)-2,2′-(octa-2,4,6-trien-1,8-diylidene)bis[1,3-dithiole-4,5-dicarbonitrile] (11e) was determined: it is a rod-like, planar molecule; in the crystal, it forms staples along the longest molecule axis. The CV measurements confirm that the redox potentials of 11, 14, and 15 decrease asymptotically with the increasing length of the spacer. Because of the close relationship of the extended tetrathiafulvalenes (ETTF's) to the carotinoids, they are named ‘caroviologenes’; they formally belong to the class of molecular wires.
    Zusätzliches Material: 11 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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