Journal of Lie Theory

no. 1
On the Dolbeault-Dirac Operators on Quantum Projective Spaces
Journal of Lie Theory, Volume 28 (2018) no. 1, pp. 211-244
We consider Dolbeault-Dirac operators on quantum projective spaces, following Krähmer and Tucker-Simmons. The main result is an explicit formula for their squares, up to terms in the quantized Levi factor, which can be expressed in terms of some central elements. This computation is completely algebraic. These operators can also be made to act on appropriate Hilbert spaces. Using the formula mentioned above, we easily find that they have compact resolvent, thus obtaining a result similar to that of D'Andrea and Dabrowski.
DOI: 10.5802/jolt.1000
Classification: 58B32, 17B37, 46L87
Keywords: Dirac operators, quantum projective spaces, quantum groups, noncommutative geometry 
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     author = {M. Matassa},
     title = {On the {Dolbeault-Dirac} {Operators} on {Quantum} {Projective} {Spaces}},
     journal = {Journal of Lie Theory},
     pages = {211--244},
     year = {2018},
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     doi = {10.5802/jolt.1000},
     zbl = {1396.58006},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1000/}
}
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M. Matassa. On the Dolbeault-Dirac Operators on Quantum Projective Spaces. Journal of Lie Theory, Volume 28 (2018) no. 1, pp. 211-244. doi: 10.5802/jolt.1000

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