Proceedings of the International Geometry Center

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Moyal and Rankin-Cohen deformations of algebras

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Published Sep 15, 2018
DOI https://doi.org/10.15673/tmgc.v11i2.1027

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Volodymyr Lyubashenko
Institute of Mathematics of NASU
http://orcid.org/0000-0002-3480-1514

Abstract

It is proven that Rankin-Cohen brackets form an associative
deformation of the algebra of polynomials whose coeffcients are holomorphic
functions on the upper half-plane.

Keywords:
Rankin-Cohen brackets, deformation

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How to Cite
Lyubashenko, V. (2018). Moyal and Rankin-Cohen deformations of algebras. Proceedings of the International Geometry Center, 11(2). https://doi.org/10.15673/tmgc.v11i2.1027
Issue
Vol 11 No 2 (2018)
Section
Papers

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References

1. Henri Cohen. Sums involving the values at negative integers of L-functions of quadratic characters. Math. Ann., 217(3):271-285, 1975.

2. Paula Beazley Cohen, Yuri I. Manin, Don Zagier. Automorphic pseudodifferential operators. In Algebraic aspects of integrable systems, volume 26 of Progr. Nonlinear Differential Equations Appl., 17-47. Birkhauser Verlag, Boston, MA, 1997.

3. Alain Connes, Henri Moscovici. Hopf algebras, cyclic cohomology and the transverse index theorem. Comm. Math. Phys., 198(1):199-246, 1998.

4. Alain Connes, Henri Moscovici. Rankin-Cohen brackets and the Hopf algebra of transverse geometry. Mosc. Math. J., 4(1):111-130, 311, 2004.

5. Amine M. El Gradechi. The Lie theory of the Rankin-Cohen brackets and allied bidifferential operators. Adv. Math., 207(2):484-531, 2006.

6. Paul A. Gordan. Vorlesungen uber Invariantentheorie. Teubner, Leipzig, 1885.

7. Valentin Ovsienko. Exotic deformation quantization. J. Differential Geom., 45(2):390-406, 1997.

8. Robert Alexander Rankin. The construction of automorphic forms from the derivatives of given forms. The Michigan Mathematical Journal, 4(2):181-186, 1957.

9. Richard Rochberg, Xiang Tang, Yijun Yao. A survey on Rankin-Cohen deformations. In Perspectives on noncommutative geometry. Proceedings of the noncommutative geometry workshop, Fields Institute, Toronto, Canada, May 27-31, 2008, 133-151. Providence, RI: American Mathematical Society (AMS); Toronto: The Fields Institute for Research in Mathematical Sciences, 2011.

10. Goro Shimura. Introduction to the arithmetic theory of automorphic functions, volume 11 of Publ. of the Math. Soc. of Japan. Iwanami Shoten, Publishers, Tokyo, 1971. Kano Memorial Lectures, No. 1.

11. Xiang Tang, Yi-Jun Yao. A universal deformation formula for H1 without projectivity assumption. Journal of Noncommutative Geometry, 3(2):151-179, 2009.

12. Don Zagier. Modular forms and differential operators. Proc. Indian Acad. Sci. Math. Sci., 104(1):57-75, 1994. K. G. Ramanathan memorial issue.