Natural and Projectively Invariant Quantizations on Supermanifolds

Leuther, Thomas; Radoux, Fabian

doi:10.3842/SIGMA.2011.034

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Natural and Projectively Invariant Quantizations on Supermanifolds

Leuther, Thomas; Radoux, Fabian

2011 • In Symmetry, Integrability and Geometry: Methods and Applications

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https://hdl.handle.net/2268/88028

DOI
10.3842/SIGMA.2011.034

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Keywords :

supergeometry; differential operators; quantization maps; projective invariance

Abstract :

[en] The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using the framework of Thomas-Whitehead connections. We extend the problem to the context of supermanifolds and adapt M. Bordemann's method in order to solve it. The obtained quantization appears as the natural globalization of the pgl(n+1|m)-equivariant quantization on Rn|m constructed by P. Mathonet and F. Radoux in [arXiv:1003.3320]. Our quantization is also a prolongation to arbitrary degree symbols of the projectively invariant quantization constructed by J. George in [arXiv:0909.5419] for symbols of degree two.

Disciplines :

Mathematics

Author, co-author :

Leuther, Thomas ; Université de Liège - ULiège > Doct. sc. (math. - Bologne)

Radoux, Fabian ; Université de Liège - ULiège > Département de mathématique > Géométrie et théorie des algorithmes

Language :

English

Title :

Natural and Projectively Invariant Quantizations on Supermanifolds

Alternative titles :

[fr] Quantifications Naturelles et Projectivement Invariantes sur les Supervariétés

Publication date :

31 March 2011

Journal title :

Symmetry, Integrability and Geometry: Methods and Applications

eISSN :

1815-0659

Publisher :

Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine, Ukraine

Special issue title :

SIGMA 7 (2011)

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://www.emis.de/journals/SIGMA/2011/034/sigma11-034.pdf

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since 31 March 2011

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Bibliography

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