The Dirac operator on compact quantum groups
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Publication:3561021
DOI10.1515/CRELLE.2010.026zbMath1218.58020arXivmath/0703161MaRDI QIDQ3561021
Lars Tuset, Sergey V. Neshveyev
Publication date: 17 May 2010
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0703161
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Geometry of quantum groups (58B32) Noncommutative global analysis, noncommutative residues (58J42)
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Cites Work
- Clifford algebra analogue of the Hopf-Koszul-Samelson theorem, the \(\rho\)-decomposition \(C({\mathfrak g})=\text{End }V_ \rho\otimes C(P)\), and the \({\mathfrak g}\)-module structure of \(\bigwedge {\mathfrak g}\)
- The Dirac operator on \(\text{SU}_{q}(2)\)
- Equivariant spectral triples on the quantum SU(2) group
- Noncommutative Riemannian and spin geometry of the standard \(q\)-sphere
- Dirac operators on quantum flag manifolds
- Spin geometry on quantum groups via covariant differential calculi
- A von Neumann algebra framework for the duality of the quantum groups
- The non-commutative Weil algebra
- A cubic Dirac operator and the emergence of Euler number multiplets of representations for equal rank subgroups
- A local index formula for the quantum sphere
- Braided chains ofq-deformed Heisenberg algebras
- Deforming maps for Lie group covariant creation and annihilation operators
- Tensor Structures Arising from Affine Lie Algebras. III
- Tensor Structures Arising from Affine Lie Algebras. IV
- CYCLIC COHOMOLOGY, QUANTUM GROUP SYMMETRIES AND THE LOCAL INDEX FORMULA FOR SU q (2)
- DRINFEL'D TWIST AND q-DEFORMING MAPS FOR LIE GROUP COVARIANT HEISENBERG ALGEBRAE
- Quantum Clifford algebras from spinor representations
- Dirac Operators on a Compact Lie Group
- Dirac operator on the Podleś sphere
- Noncommutative manifolds, the instanton algebra and isospectral deformations
