Nichols Algebras and Quantum Principal Bundles

Abstract

We introduce a general framework for associating to a homogeneous quantum principal bundle a Yetter-Drinfeld module structure on the cotangent space of the base calculus. The holomorphic and anti-holomorphic Heckenberger-Kolb calculi of the quantum Grassmannians are then presented in this framework. This allows us to express the calculi in terms of the corresponding Nichols algebras. The extension of this result to all irreducible quantum flag manifolds is then conjectured.

Updated references

References in corpus (6)

• Gauge theory on noncommutative Riemannian principal bundles
• Holomorphic Relative Hopf Modules over the Irreducible Quantum Flag Manifolds
• Antipodes, preantipodes and Frobenius functors
• Positive Line Bundles Over the Irreducible Quantum Flag Manifolds
• An algebraic framework for noncommutative bundles with homogeneous fibres
• Root groupoid and related Lie superalgebras

Cited by in corpus (3)

• Noncommutative differential geometry on crossed product algebras
• Quantised ${\mathfrak{sl}}_2$-differential algebras
• Group valued moment maps for even and odd simple $G$-modules