Quantized symplectic oscillator algebras of rank one
نویسندگان
چکیده
منابع مشابه
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.
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With a nilpotent element in a semisimple Lie algebra g one associates a finitely generated associative algebra W called a W -algebra of finite type. This algebra is obtained from the universal enveloping algebra U(g) by a certain Hamiltonian reduction. We observe that W is the invariant algebra for an action of a reductive group G with Lie algebra g on a quantized symplectic affine variety and ...
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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...
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We give a classification theorem for unital separable nuclear simple C∗-algebras with tracial rank no more than one. Let A and B be two unital separable simple nuclear C∗-algebras with TR(A), TR(B) ≤ 1 which satisfy the universal coefficient theorem. We show that A ∼= B if and only if there is an order and unit preserving isomorphism γ = (γ0, γ1, γ2) : (K0(A),K0(A)+, [1A],K1(A), T (A)) ∼= (K0(B...
متن کاملOn Lie Algebras of Rank One(')
where h is any additive mapping of G into F (see [1, p. 138]). Each of these algebras is a simple Lie algebra, for which u0 spans a one-dimensional Cartan subalgebra, with one-dimensional root spaces spanned by the ux. We shall prove that under certain hypotheses, these are the only Lie algebras over F of rank one. Kaplansky in [5] has proved that any restricted simple Lie algebra over F of ran...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2006.06.051