Distributions on graded manifolds. (English) Zbl 0955.58006
In this paper, distributions on a graded manifold whose underlying manifold is orientable are defined as linear forms on the spaces of sections with compact support of the Berezinian sheaf; here linearity is taken with respect to the natural structure of right module of the Berezinian sheaf. The author first gives a description of distributions on open subsets with graded coordinates and explicitely writes the formula for graded coordinate changes. A global expression in terms of ordinary distributions taking values in quotient of a sheaf of top form-valued differential operators on the Berezinian sheaf is also given. The case of non-orientable underlying manifold is considered in the last section of the paper.
Reviewer: Daniel Hernandez Ruiperez (Salamanca)
MSC:
58C50 | Analysis on supermanifolds or graded manifolds |
58A50 | Supermanifolds and graded manifolds |
46F05 | Topological linear spaces of test functions, distributions and ultradistributions |
46F10 | Operations with distributions and generalized functions |