Skip to main content
Log in

Infinitesimal Deformation Quantization of Complex Analytic Spaces

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

The quantization problem for analytic algebras and for complex analytic spaces is discussed. The construction of Hochschild cohomology is modified for this category. It is proved that this cohomology is always a coherent analytic sheaf in each degree.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Barr M. (1968). Harrison cohomology, Hochschild cohomology and triples. J. Algebra 8: 314–323

    Article  MATH  MathSciNet  Google Scholar 

  2. Berezin F.A. (1975). General concept of quantization. Comm. Math. Phys. 40: 153–174

    Article  ADS  MathSciNet  Google Scholar 

  3. Dito, G., Sternheimer, D.: Deformation quantization: genesis, developments and metamorphoses. Deformation quantization (Strasbourg 2001). IRMA Lect. Math. Theor. Phys. 1, 9–54 (2002) Walter de Gruyter, Berlin (math.QA/0201168)

  4. Frønsdal, Ch., Kontsevich, M.: Quantization on curves. ArXiv:math-ph/0507021

  5. Gerstenhaber M. and Schack S.D. (1987). A Hodge-type decomposition for commutative algebra cohomology. J. Pure Appl. Algebra 48: 229–247

    Article  MATH  MathSciNet  Google Scholar 

  6. Hochschild G., Kostant B. and Rosenberg A. (1962). Differential forms on regular affine algebras. Trans. Amer. Math. Soc. 102: 383–408

    Article  MATH  MathSciNet  Google Scholar 

  7. Kontsevich, M.: Deformation quantization of algebraic varieties. Lett. Math. Phys. 56(3), 271–294 (2001) (ArXiv:math.AG/0106006)

    Google Scholar 

  8. Palamodov V.P. (1983). Cohomology of analytic algebras. Trans. Moscow Math. Soc. N2: 1–61

    Google Scholar 

  9. Palamodov V.P. (1976). Deformation of complex spaces. Russian Math. Surveys 31: 129–197

    Article  MathSciNet  Google Scholar 

  10. Sternheimer D. (2005). Quantization: deformation and/or functor. Lett. Math. Phys. 74: 293–309

    Article  MATH  MathSciNet  Google Scholar 

  11. Tyurina G.N. (1969). Locally semiuniversal flat deformations of isolated singularities of complex spaces (English). Math. USSR, Izv. 3: 967–999

    Article  MATH  Google Scholar 

  12. Yekutieli, A.: Deformation quatization in algebraic geometry. Adv. Math. 198(1), 383–432 (2005) (ArXiv:math.AG/0310399)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Victor P. Palamodov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Palamodov, V.P. Infinitesimal Deformation Quantization of Complex Analytic Spaces. Lett Math Phys 79, 131–142 (2007). https://doi.org/10.1007/s11005-006-0139-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11005-006-0139-6

Mathematics Subject Classification (2000)

Keywords

Navigation