A cohomology decomposition theorem

A Cohomology Decomposition Theorem

In [9] Jackowski and McClure gave a homotopy decomposition theorem for the classifying space of a compact Lie group G; their theorem states that for any prime p the space BG can be constructed at p as the homotopy direct limit of a specific diagram involving the classifying spaces of centralizers of elementary abelian p-subgroups of G. In this paper we will prove a parallel algebraic decomposit...

Brst Cohomology and Hodge Decomposition Theorem in Abelian Gauge Theory

We discuss the Becchi-Rouet-Stora-Tyutin (BRST) cohomology and Hodge decomposition theorem for the two dimensional free U(1) gauge theory. In addition to the usual BRST charge, we derive a local, conserved and nilpotent co(dual)-BRST charge under which the gauge-fixing term remains invariant. We express the Hodge decomposition theorem in terms of these charges and the Laplacian operator. We tak...

A Mackey Decomposition Theorem and Cohomology for Quantum Groups at Roots of 1

Introduction This is a continuation of the investigation in [L3] into the module structure of those modules for quantum enveloping algebras U analogous to the coho-mology groups of line bundles on the flag varieties for semisimple algebraic groups. In [L3], we used the admissible categories for Hopf algebras and their induction theory and proved a modified Borel-Bott-Weil theorem for R l(w) Ind

A Martingale Decomposition Theorem

A Hochschild Cohomology Comparison Theorem for Prestacks

We generalize and clarify Gerstenhaber and Schack’s “Special Cohomology Comparison Theorem”. More specifically we obtain a fully faithful functor between the derived categories of bimodules over a prestack over a small category U and the derived category of bimodules over its corresponding fibered category. In contrast to Gerstenhaber and Schack we do not have to assume that U is a poset.