2011/09/14 by Alexander Alldridge, Alldridge, Alexander
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Representation Theory (math.RT) #math-ph #math.DG #math.MP #math.RT
paper · pdf · doi:10.48550/arxiv.1109.3161
32 pages
arxiv created 2011/09/14 · openalex publication_date 2011/09/14 · arxiv updated 2011/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
With a view towards applications in the theory of infinite-dimensional representations of finite-dimensional Lie supergroups, we introduce a new category of supermanifolds. In this category, supermanifolds of `maps' and `fields' (fibre bundle sections) exist. In particular, loop supergroups can be realised globally in this framework. It also provides a convenient setting for induced representations of supergroups, allowing for a version of Frobenius reciprocity. Finally, convolution algebras of finite-dimensional Lie supergroups are introduced and applied to a prove a supergroup Dixmier-Malliavin Theorem: The space of smooth vectors of a continuous representation of a supergroup pair equals the Garding space given by the convolution with compactly supported smooth supergroup densities.