Vanishing of one dimensional L-cohomologies of loop groups
نویسنده
چکیده
Let G be a simply connected compact Lie group. Let Le(G) be the based loop group with the base point e which is the identity element. Let νe be the pinned Brownian motion measure on Le(G) and let α ∈ L(∧T Le(G), νe) ∩ D∞,p(∧1T Le(G), νe) (1 < p < 2) be a closed 1-form on Le(G). Using the results in rough path analysis, we prove that there exists an f ∈ Lloc(Le(G), νe) such that df = α. Moreover we prove that dimker¤ = 0 for the Hodge-Kodaira type operator acting on 1-forms on Le(G).
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تاریخ انتشار 2009