Quantized Symplectic Oscillator Algebras of Rank One
نویسنده
چکیده
A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with Uq(sl2). We study its representation theory, and in particular, its category O.
منابع مشابه
ar X iv : m at h / 04 05 17 6 v 3 [ m at h . R T ] 1 7 N ov 2 00 4 QUANTIZED SYMPLECTIC OSCILLATOR ALGEBRAS OF RANK ONE
A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with Uq(sl2). We study its representation theory, and in particular, its category O.
متن کاملar X iv : m at h / 04 05 17 6 v 4 [ m at h . R T ] 1 6 Ju n 20 06 QUANTIZED SYMPLECTIC OSCILLATOR ALGEBRAS OF RANK ONE
A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with Uq(sl2). We study its representation theory, and in particular, its category O.
متن کاملA Class of Quadratic Matrix Algebras Arising from the Quantized Enveloping Algebra
A natural family of quantized matrix algebras is introduced. It includes the two best studied such. Located inside Uq(A2n−1), it consists of quadratic algebras with the same Hilbert series as polynomials in n variables. We discuss their general properties and investigate some members of the family in great detail with respect to associated varieties, degrees, centers, and symplectic leaves. Fin...
متن کاملA Class of Quadratic Matrix Algebras
A natural family of quantized matrix algebras is introduced. It includes the two best studied such. Located inside U q (A 2n?1), it consists of quadratic algebras with the same Hilbert series as polynomials in n 2 variables. We discuss their general properties and investigate some members of the family in great detail with respect to associated varieties, degrees, centers, and symplectic leaves...
متن کاملOscillator Realization of Higher-U(N+, N−)-Spin Lie Algebras of W∞-type and Quantized Symplectic Diffeomorphisms
This article is a further contribution to our research [1] into a class of infinite-dimensional Lie algebras L∞(N+, N−) generalizing the standard W∞ algebra, viewed as a tensor operator algebra of SU(1, 1) in a group-theoretic framework. Here we interpret L∞(N+, N−) either as a infinite continuation of pseudo-unitary symmetries U(N+, N−), or as a “higher-U(N+, N−)-spin extension” of the diffeom...
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 2004