ON THE DEFORMATION QUANTIZATION OF AFFINE ALGEBRAIC VARIETIES
Abstract
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.
References
- Ann. Phys. 111(1), 61 (1978). Crossref, ISI, Google Scholar
- Lett. Math. Phys. 7, 487 (1983). Crossref, ISI, Google Scholar
-
S. Lang , Algebra ( Addison Wesley , 1993 ) . Google Scholar - Pacific J. Math. 20(2), 197 (1967). Crossref, ISI, Google Scholar
- J. Differential Geom. 40(2), 213 (1994). Crossref, ISI, Google Scholar
- I. Selecta Math., New Series 2(1), 1 (1996). Crossref, ISI, Google Scholar
- M. Kontsevich, Deformation quantization of Poisson manifolds, math.QA/9709040 . Google Scholar
- Amer. J. Math. 86, 271 (1964). ISI, Google 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
- Lett. Math. Phys. 56(3), 271 (2001). Crossref, ISI, Google 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
- Pacific J. Math. 198(2), 411 (2001). Crossref, ISI, Google Scholar
- Lett. Math. Phys. 58, 57 (2001). Crossref, Google Scholar
- Pacific J. Math. 206(2), 321 (2002). Crossref, ISI, Google Scholar
- J. Phys. A: Math. Gen. 35, 5687 (2002). Crossref, Google Scholar
- J. Hoppe, Quantum theory of a massless relativistic surface and a two-dimensional bound state problem, MIT PhD thesis (1982) . Google Scholar
- Duke Math. J. 115(2), 329 (2002). ISI, Google Scholar
- A. Cattaneo, G. Felder and L. Tomassini, Fedosov connections on jet bundles and deformation quantization (2001) . Google Scholar
- Soviet Math. Dokl. 12(5), 1367 (1971). ISI, Google Scholar
-
M. F. Atiyah and I. G. McDonald , Introduction to Commutative Algebra ( Perseus Publishing , 1994 ) . Google Scholar