Orientation in operator algebras

A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics.

Contributions of distinct quaternary contacts to cooperative operator binding by Mnt repressor

Mnt, a tetrameric repressor encoded by bacteriophage P22, uses N-domain dimers to contact each half of its operator site. Experiments with a double mutant and structural homology with the P22 Arc repressor suggest that contacts made by Arg-28 and stabilized by Glu-33 are largely responsible for dimer–dimer cooperativity in Mnt. These dimer–dimer contacts are energetically more important for operator binding than solution tetramerization, which is mediated by an independent C-terminal coiled-coil domain. Indeed, once one dimer of the Mnt tetramer contacts an operator half site, binding of the second dimer occurs with an effective concentration much lower than that expected if both dimers were flexibly tethered. These results suggest that binding of the second dimer introduces some strain into the protein–DNA complex, a mechanism that could serve to limit the affinity of operator binding and to prevent strong binding of the Mnt tetramer to nonoperator sites.

The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

On the coefficients of the characteristic series of the U-operator

A conceptual proof is given of the fact that the coefficients of the characteristic series of the U-operator acting on families of overconvegent modular forms lie in the Iwasawa algebra.