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  - 
TY  - THES
A1  - Dippell, Marvin
T1  - Constraint Reduction in Algebra, Geometry and Deformation Theory
T1  - Constraint Reduktion in Algebra, Geometrie und Deformationsquantisierung
N2  - 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.
N2  - Um koisotrope Reduktion im Kontext der Deformationsquantisierung zu betrachten, werden constraint Mannigfaltigkeiten und constraint Algebren als grundlegende Objekte definiert. Wichtige Eigenschaften verschiedener zugehöriger Kategorien, sowie deren Kompatibilität mit Reduktion werden untersucht. In Analogie zum klassischen Serre-Swan-Theorem können constraint Vektorbündel mit bestimmten endlich erzeugt projektiven constraint Moduln identifiziert werden. Außerdem wird ein Symbolkalkül für constraint Multidifferenzialoperatoren eingeführt. Nach der Entwicklung der allgemeinen Deformationstheorie von constraint Algebren mithilfe von constraint Hochschild Kohomologie und constraint differentiell gradierten Lie-Algebren, wird die zweite constraint Hochschild Kohomologie im Fall eines endlich dimensionalen constraint Vektorraums berechnet.
KW  - Differentialgeometrie
KW  - Deformationsquantisierung
KW  - Coisotropic reduction
KW  - Symplektische Geometrie
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-301670
ER  -