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We introduce the notion of central extension of gerbes on a topological space. We then show that there are obstruction classes to lifting objects and isomorphisms in a central extension. We also discuss pronilpotent gerbes. These results are used in a subsequent paper to study twisted deformation quantization on algebraic varieties.
Given a central extension of Lie groups, we study the classification problem of lifting the structure group together with a given connection. For reductive structure groups we introduce a new connective structure on the lifting gerbe associated to th
We use Segal-Mitchisons cohomology of topological groups to define a convenient model for topological gerbes. We introduce multiplicative gerbes over topological groups in this setup and we define its representations. For a specific choice of represe
We introduce an axiomatic framework for the parallel transport of connections on gerbes. It incorporates parallel transport along curves and along surfaces, and is formulated in terms of gluing axioms and smoothness conditions. The smoothness conditi
This is an old paper put here for archeological purposes. We compute the second cohomology of current Lie algebras of the form $Lotimes A$, where $L$ belongs to some class of Lie algebras which includes classical simple and Zassenhaus algebras, and o
The aim of this paper is to study the $(alpha, gamma)$-prolongation of central extensions. We obtain the obstruction theory for $(alpha, gamma)$-prolongations and classify $(alpha, gamma)$-prolongations thanks to low-dimensional cohomology groups of groups.