It is widely accepted that small quantum groups should possess a quasitriangular structure, even though this is technically not true. In this article we construct explicit Rmatrices, sometimes several inequivalent ones, over certain natural extensions of small quantum groups by grouplike elements. The extensions are in correspondence to lattices between root and weight lattice. Our result generalizes a well-known calculation for u q (sl 2 ) used in logarithmic conformal field theories.

Abstract. Using combinatorics and character theory, we determine the imprimitive faithful complex characters, i.e., the irreducible faithful complex characters which are induced from proper subgroups, of the Schur covers of the symmetric and alternating groups. Furthermore, for every imprimitive character we establish all its minimal block stabilizers. As a corollary, we also determine the monomial faithful characters of the Schur covers.

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This research aims to give an overview on how to improve the biogas yeild in Balinese digester plants using various co-substrates which are available in Bali. A series testing on the digestibility of substrates were set up either in the field or in the biogas laboratory. In-field analyses like testing the CO2-content and taking samples from digested manure were undertaken. Analyses such as dry matter (DM) and organic dry matter (oDM) determination, pH measurement and FOS/TAC were handled in the biogas laboratory. The huge number of different fruits in Bali gives a good opportunity to use their wastes like Durian hulls and Banana peelings, which can not be used anymore, as co-substrates in biogas plants. The results of these investigations allow to estimate the additional biogas yield, when adding co-substrates to a cow manure biogas plant.