@article{HeinsRothWaldmann2023,
  author    = {Heins, Michael and Roth, Oliver and Waldmann, Stefan},
  title     = {Convergent star products on cotangent bundles of Lie groups},
  series = {Mathematische Annalen},
  volume    = {386},
  journal   = {Mathematische Annalen},
  number    = {1-2},
  issn      = {0025-5831},
  doi       = {10.1007/s00208-022-02384-x},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324324},
  pages     = {151-206},
  year      = {2023},
  abstract  = {For a connected real Lie group G we consider the canonical standard-ordered star product arising from the canonical global symbol calculus based on the half-commutator connection of G. This star product trivially converges on polynomial functions on T\(^*\)G thanks to its homogeneity. We define a nuclear Fr{\´e}chet algebra of certain analytic functions on T\(^*\)G, for which the standard-ordered star product is shown to be a well-defined continuous multiplication, depending holomorphically on the deformation parameter \(\hbar\). This nuclear Fr{\´e}chet algebra is realized as the completed (projective) tensor product of a nuclear Fr{\´e}chet algebra of entire functions on G with an appropriate nuclear Fr{\´e}chet algebra of functions on \({\mathfrak {g}}^*\). The passage to the Weyl-ordered star product, i.e. the Gutt star product on T\(^*\)G, is shown to preserve this function space, yielding the continuity of the Gutt star product with holomorphic dependence on \(\hbar\).},
  language  = {en}
}
@article{DippellEspositoWaldmann2022,
  author    = {Dippell, Marvin and Esposito, Chiara and Waldmann, Stefan},
  title     = {Deformation and Hochschild cohomology of coisotropic algebras},
  series = {Annali di Matematica Pura ed Applicata},
  volume    = {201},
  journal   = {Annali di Matematica Pura ed Applicata},
  number    = {3},
  doi       = {10.1007/s10231-021-01158-7},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-329069},
  pages     = {1295-1323},
  year      = {2022},
  abstract  = {Coisotropic algebras consist of triples of algebras for which a reduction can be defined and unify in a very algebraic fashion coisotropic reduction in several settings. In this paper, we study the theory of (formal) deformation of coisotropic algebras showing that deformations are governed by suitable coisotropic DGLAs. We define a deformation functor and prove that it commutes with reduction. Finally, we study the obstructions to existence and uniqueness of coisotropic algebras and present some geometric examples.},
  language  = {en}
}