Die Zürcher Vorlesung von Schur über Darstellungstheorie

Im Jahre 1936, unmittelbar nach seiner Entlassung als Professor in Berlin, wurde Issai Schur an die ETH in Zürich eingeladen, um eine Vorlesung über die Darstellungstheorie von Gruppen zu halten. Die (kurze) Vorlesung wurde damals vom jungen Eduard Stiefel ausgearbeitet und in vervielfältigter Form herausgegeben. Es handelt sich dabei historisch um den ersten Lehrbuch-Text überhaupt, der ganz der Darstellungstheorie gewidmet war. Im vorliegenden Beitrag werden die Hintergründe der Einladung von Schur an die ETH beleuchtet, es wird ein Überblick über den Inhalt des Textes gegeben und schliesslich wird die damalige Veröffentlichung in einen historischen Bezug gesetzt.Der vorliegende Text ist eine leichte Überarbeitung eines Vortrages im Rahmen der Kolloquiums History of Mathematics; Algebra, Geometry and Number Theory and their Interactions, 10./11. Januar 2003, ETH Zürich.     

Finiteness of $$\pi _1$$-sensitive Hofer–Zehnder capacity and equivariant loop space homology

We prove that if M is a closed, connected, oriented, rationally inessential manifold, then the Hofer–Zehnder capacity of the unit disk bundle of the cotangent bundle of M is finite.     

Tetraaquabis(carbamoyldicyanomethanido‐κN)manganese(II) dihydrate

The crystal structure of [Mn(C₄H₂N₃O)₂(H₂O)₄]·2H₂O, conventionally abbreviated [Mn(cdm)₂(H₂O)₄]·2H₂O, where cdm is carbamoyldi­cyano­methanide, is described. The bond lengths and distances are comparable to those previously reported for the isomorphous Ni and Co analogs. Molecular units are formed by coordination of the nitrile N atoms of two cdm anions and four water mol­ecules to the manganese(II) cation. Although these mononuclear molecular species are connected via hydrogen bonding, no magnetic ordering was observed down to 1.55 K.     

KMnAg3(CN)6, a new triply interpenetrating network solid

The single‐crystal structure of potassium manganese tris­[di­cyano­argentate(I)], KMnAg₃(CN)₆, is described. This is the first Mn‐containing example of the triply interpenetrating MAg₃(CN)₆ type. The K⁺ ion is found to be located in an ordered manner on one of two possible interstitial sites, leading to a chiral space group.     

catena‐Poly[[diaquamanganese(II)]‐di‐μ‐1,1,3,3‐tetracyano‐2‐ethoxypropenido‐κ4N1:N3]

The crystal structure of the title compound, [Mn(C₉H₅N₄O)₂(H₂O)₂], conventionally denoted Mn(EtO‐TCA)₂(H₂O)₂, where EtO‐TCA is 2‐ethoxy‐1,1,3,3‐tetra­cyano­propenide, is described. The EtO‐TCA anions bridge Mn^II centers through one of the nitrile N atoms of each of their two di­cyano­methanide groups, thus forming dibridged chains along ab. These chains are linked into two‐dimensional sheets through hydrogen bonding. The seven‐atom bridge, which results in a long Mn⃛Mn intrachain interaction [9.0044 (4) Å], as well as the large interchain separations [8.3288 (4) and 8.5220 (4) Å] prohibit long‐range magnetic ordering down to temperatures as low as 1.55 K.     

Polymerisation of cyclic monomers, 8. Synthesis and radical polymerisation of hybrid 2‐vinylcyclopropanes

Hybrid 2‐vinylcyclopropanes were synthesised by the esterification of 1‐methoxycarbonyl‐2‐vinylcyclopropane‐1‐carboxylic acid with hydroxy group containing (meth)acrylates in the presence of 1,3‐dicyclohexylcarbodiimide (DCC). The structure of the new hybrid monomers was confirmed by elemental analysis, IR, ¹H NMR and ¹³C NMR spectroscopy. The radical polymerisation of the hybrid monomers in bulk with 2,2'‐azoisobutyronitrile (AIBN) results in transparent cross‐linked polymers, whereas solution polymerisation partially results in soluble polymers with pendant 2‐vinylcyclopropyl groups.     

Low‐temperature tris(tert‐butyl 3‐oxo­butan­oato)­iron(III)

The low‐temperature (173 K) structure of the title complex, [Fe(C₈H₁₃O₃)₃], a metal–organic chemical vapour deposition (MOCVD) precursor, has been analyzed. The Fe atom is octahedrally coordinated and the three chelate rings are found to be significantly non‐planar, adopting a half‐chair conformation with the Fe atom out of the plane.