@phdthesis{Dippell2023,
  author    = {Dippell, Marvin},
  title     = {Constraint Reduction in Algebra, Geometry and Deformation Theory},
  doi       = {10.25972/OPUS-30167},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-301670},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2023},
  abstract  = {To study coisotropic reduction in the context of deformation quantization we introduce constraint manifolds and constraint algebras as the basic objects encoding the additional information needed to define a reduction. General properties of various categories of constraint objects and their compatiblity with reduction are examined. A constraint Serre-Swan theorem, identifying constraint vector bundles with certain finitely generated projective constraint modules, as well as a constraint symbol calculus are proved. After developing the general deformation theory of constraint algebras, including constraint Hochschild cohomology and constraint differential graded Lie algebras, the second constraint Hochschild cohomology for the constraint algebra of functions on a constraint flat space is computed.},
  subject      = {Differentialgeometrie},
  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}
}