World Scientific
  • Search
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
×
Our website is made possible by displaying certain online content using javascript.
In order to view the full content, please disable your ad blocker or whitelist our website www.worldscientific.com.

System Upgrade on Tue, Oct 25th, 2022 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at [email protected] for any enquiries.

ON THE DEFORMATION QUANTIZATION OF AFFINE ALGEBRAIC VARIETIES

    We compute an explicit algebraic deformation quantization for an affine Poisson variety described by an ideal in a polynomial ring, and inheriting its Poisson structure from the ambient space.

    AMSC: 53D55, 14A22

    References

    • F. Bayenet al., Ann. Phys. 111(1), 61 (1978). Crossref, ISIGoogle Scholar
    • M. De Wilde and P. B. A. Lecomte, Lett. Math. Phys. 7, 487 (1983). Crossref, ISIGoogle Scholar
    • S.   Lang , Algebra ( Addison Wesley , 1993 ) . Google Scholar
    • E. Davis, Pacific J. Math. 20(2), 197 (1967). Crossref, ISIGoogle Scholar
    • B. Fedosov, J. Differential Geom. 40(2), 213 (1994). Crossref, ISIGoogle Scholar
    • P. Etingof and D. A. Kazhdan, I. Selecta Math., New Series 2(1), 1 (1996). Crossref, ISIGoogle Scholar
    • M. Kontsevich, Deformation quantization of Poisson manifolds, math.QA/9709040 . Google Scholar
    • B. Kostant, Amer. J. Math. 86, 271 (1964). ISIGoogle Scholar
    • D. E. Tamarkin, Another proof of M. Kontsevich formality theorem, math.QA/ 9803025; Formality of chain operad of small squares, math.QA/9809164 . Google Scholar
    • M. Koutsevich, Lett. Math. Phys. 56(3), 271 (2001). Crossref, ISIGoogle Scholar
    • A. Yekutieli, On deformation quantization in algebraic geometry, math. AG/0310399 . Google Scholar
    • R. Bezrukavnikov and D. Kaledin, Fedosov quantization in algebraic context, math.AG/0309290A. Yekutieli, On deformation quantization in algebraic geometry, math. AG/0310399 . Google Scholar
    • M. Cahen, S. Gutt, Produits * sur les orbites des groupes semi-simples de rang 1, C. R. Acad. Sci. Paris 296 (1983), 821–823; An algebraic construction of * product on the regular orbits of semisimple Lie groups, in Gravitation and Cosmology, A Volume in Honor of Ivor Robinson, eds W. Rundler and A. Trautman, Monographs and Textbooks in Physical Sciences (Bibliopolis 1987); Non localité d'une déformation symplectique sur la sphère S2, Bull. Soc. Math. Belg. B36 (1987) 207–221 . Google Scholar
    • R. Fioresi and M. A. Lledó, Pacific J. Math. 198(2), 411 (2001). Crossref, ISIGoogle Scholar
    • M. A. Lledó, Lett. Math. Phys. 58, 57 (2001). CrossrefGoogle Scholar
    • R. Fioresi, A. Levrero and M. A. Lledó, Pacific J. Math. 206(2), 321 (2002). Crossref, ISIGoogle Scholar
    • R. Fioresi and M. A. Lledó, J. Phys. A: Math. Gen. 35, 5687 (2002). CrossrefGoogle Scholar
    • J. Hoppe, Quantum theory of a massless relativistic surface and a two-dimensional bound state problem, MIT PhD thesis (1982) . Google Scholar
    • G. Cattaneo, G. Felder and L. Tomassini, Duke Math. J. 115(2), 329 (2002). ISIGoogle Scholar
    • A. Cattaneo, G. Felder and L. Tomassini, Fedosov connections on jet bundles and deformation quantization (2001) . Google Scholar
    • I. M. Gelfand and D. A. Kazhdan, Soviet Math. Dokl. 12(5), 1367 (1971). ISIGoogle Scholar
    • M. F.   Atiyah and I. G.   McDonald , Introduction to Commutative Algebra ( Perseus Publishing , 1994 ) . Google Scholar