De Rham complex for quantized irreducible flag manifolds
By István Heckenberger, S. Kolb. 2003
77 citations recorded by the source corpus.
It is shown that quantized irreducible flag manifolds possess a canonical q-analogue of the de Rham complex. Generalizing the well-known situation for the standard Podleś' quantum sphere this analogue is obtained as the universal differential calculus of a distinguished first order differential calculus. The corresponding differential d can be written as a sum of differentials ∂ and ∂¯. The universal differential calculus corresponding to the first order differential calculi d, ∂, and ∂¯ are given in terms of generators and relations. Relations to well-known quantized exterior algebras are established. The dimensions of the homogeneous components are shown to be the same as in the classical case. The existence of a volume form is proven.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/438c0729f3ab70a7676e4627799af3c37ab61ac7
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Citations in the corpus
- Noncommutative complex differential geometry (2012, methodology): “In [43,5,6], Kolb and Heckenberger construct an integrable almost complex structure on the quantum group analogues of irreducible flag varieties.”
- Noncommutative K\"ahler Structures on Quantum Homogeneous Spaces (2011, background): “Moreover, the subfamily of irreducible quantum flag manifolds comes endowed with a differential calculus, the Heckenberger–Kolb calculus, which is uniquely characterised by a simple set of natural axioms [13, 14].”
- On the Hochschild (co)homology of quantum homogeneous spaces (2008, unknown): “, in [7, 19, 18, 17, 25, 39].”