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تسجيل مستخدم جديدBraided Commutative Geometry and Drinfeld Twist Deformations
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تأليف
Thomas Weber
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In this thesis we give obstructions for Drinfeld twist deformation quantization on several classes of symplectic manifolds. Motivated from this quantization procedure, we further construct a noncommutative Cartan calculus on any braided commutative algebra, as well as an equivariant Levi-Civita covariant derivative for any non-degenerate equivariant metric. This generalizes and unifies the Cartan calculus on a smooth manifold and the Cartan calculus on twist star product algebras. We prove that the Drinfeld functor leads to equivalence classes in braided commutative geometry and commutes with submanifold algebra projection.
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We construct a noncommutative Cartan calculus on any braided commutative algebra and study its applications in noncommutative geometry. The braided Lie derivative, insertion and de Rham differential are introduced and related via graded braided commu
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