TY  - JOUR
A1  - Heins, Michael
A1  - Roth, Oliver
A1  - Waldmann, Stefan
T1  - Convergent star products on cotangent bundles of Lie groups
JF  - Mathematische Annalen
N2  - 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 Fréchet 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 Fréchet algebra is realized as the completed (projective) tensor product of a nuclear Fréchet algebra of entire functions on G with an appropriate nuclear Fréchet 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 \(\hbar\).
KW  - Lie groups
KW  - star products
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-324324
SN  - 0025-5831
VL  - 386
IS  - 1-2
ER  - 
TY  - JOUR
A1  - Dippell, Marvin
A1  - Esposito, Chiara
A1  - Waldmann, Stefan
T1  - Deformation and Hochschild cohomology of coisotropic algebras
JF  - Annali di Matematica Pura ed Applicata
N2  - 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.
KW  - deformation theory
KW  - differential graded Lie algebra
KW  - coisotropic reduction
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-329069
VL  - 201
IS  - 3
ER  -