On quantization of quadratic Poisson structures
نویسنده
چکیده
Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel’d [Dr], [Gr]. We exhibit in this article an example of quadratic Poisson structure which does not arise this way.
منابع مشابه
ar X iv : q - a lg / 9 70 80 12 v 1 1 2 A ug 1 99 7 Star Products for integrable Poisson Structures on
We prove the existence of a deformation quantization for integrable Poisson structures on R 3 and give a generalization for a special class of three dimensional manifolds. The program of deformation quantization of the function algebra on a sym-plectic manifold extends naturally to manifolds with nonregular Poisson structures. In contrast to symplectic manifolds the existence of star products o...
متن کاملKoszul duality in deformation quantization and Tamarkin’s approach to Kontsevich formality
Let α be a quadratic Poisson bivector on a vector space V . Then one can also consider α as a quadratic Poisson bivector on the vector space V ∗[1]. Fixed a universal deformation quantization (prediction of some complex weights to all Kontsevich graphs [K97]), we have deformation quantization of the both algebras S(V ∗) and Λ(V ). These are graded quadratic algebras, and therefore Koszul algebr...
متن کاملفرمولبندی هندسی کوانتش تغییرشکل برزین
In this paper we try to formulate the Berezin quantization on projective Hilbert space P(H) and use its geometric structure to construct a correspondence between a given classical theory and a given quantum theory. It wil be shown that the star product in berezin quantization is equivalent to the Posson bracket on coherent states manifold M, embodded in P(H), and the Berezin method is used to...
متن کاملA quadratic Poisson Gel’fand-Kirillov problem in prime characteristic
The quadratic Poisson Gel’fand-Kirillov problem asks whether the field of fractions of a Poisson algebra is Poisson birationally equivalent to a Poisson affine space, i.e. to a polynomial algebra K[X1, . . . , Xn] with Poisson bracket defined by {Xi, Xj} = λijXiXj for some skew-symmetric matrix (λij) ∈ Mn(K). This problem was studied in [9] over a field of characteristic 0 by using a Poisson ve...
متن کاملv 1 9 J an 1 99 5 Quantization of Poisson pencils and generalized Lie algebras
We describe two types of Poisson pencils generated by a linear bracket and a quadratic one arising from a classical R-matrix. A quantization scheme is discussed for each. The quantum algebras are represented as the enveloping algebras of " generalized Lie algebras " .
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008