We provide the Cartan calculus for bicovariant differential forms on bicrossproduct quantum groups $k(M)\lrbicross kG$ associated to finite group factorizations and a field . The irreducible calculi are associated to certain conjugacy classes in and representations of isotropy groups. We find the full ext…
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4 results for “bicrossproduct”
Geometrically explains Lie 2-algebroids and their connections.
problem Exploring Lie 2-algebroids and their geometric properties.
method Explains Li-Bland's correspondence and uses geometric equivalence.
result Proves bicrossproduct of matched pairs of 2-representations is a split Lie 2-algebroid.
Quantum Jet Bundlesmath.QA
Formulates quantum jet bundles over noncommutative algebras with connections and braiding.
problem Defining jet bundles over noncommutative algebras with connections and braiding.
method Formalizes jet bundles over noncommutative algebras with flat connections and braiding tensor obeying Yang-Baxter equation.
result Examples include permutation groups, matrix algebras, and quantum spacetime models.
We study noncommutative bundles and Riemannian geometry at the semiclassical level of first order in a deformation parameter , using a functorial approach. The data for quantisation of the cotangent bundle is known to be a Poisson structure and Poisson preconnection and we now show that this data defines to a functo…