scholarly journals UNITARY REPRESENTATIONS FOR THE SCHRÖDINGER–VIRASORO LIE ALGEBRA

2012 ◽  
Vol 12 (01) ◽  
pp. 1250132 ◽  
Author(s):  
XIUFU ZHANG ◽  
SHAOBIN TAN
Keyword(s):  
Lie Algebra ◽  
Virasoro Algebra ◽  
Unitary Representations

In this paper, conjugate-linear anti-involutions and unitary Harish-Chandra modules over the Schrödinger–Virasoro algebra are studied. It is proved that there are only two classes conjugate-linear anti-involutions over the Schrödinger–Virasoro algebra. The main result of this paper is that a unitary Harish-Chandra module over the Schrödinger–Virasoro algebra is simply a unitary Harish-Chandra module over the Virasoro algebra.

Derivations and Automorphism Group of Original Deformative Schrödinger-Virasoro Algebra

2015 ◽  
Vol 22 (03) ◽  
pp. 517-540 ◽  
Author(s):  
Qifen Jiang ◽  
Song Wang
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Direct Product ◽  
Virasoro Algebra ◽  
Witt Algebra ◽  
Tensor Density ◽  
Derivation Algebra

In this paper, we determine the derivation algebra and the automorphism group of the original deformative Schrödinger-Virasoro algebra, which is the semi-direct product Lie algebra of the Witt algebra and its tensor density module Ig(a,b).

EXTENDED BOTT–VIRASORO ALGEBRA, SEMIDIRECT PRODUCT, ⋆-LIE ALGEBRA OF DIFFEOMORPHISM AND NONCOMMUTATIVE INTEGRABLE SYSTEMS

2009 ◽  
Vol 06 (04) ◽  
pp. 555-572
Author(s):  
PARTHA GUHA
Keyword(s):  
Lie Algebra ◽  
Semidirect Product ◽  
Virasoro Algebra ◽  
Lie Derivative ◽  
Coadjoint Representation ◽  
Kdv Equations ◽  
Two Component ◽  
Universal Extension ◽  
Product Algebra ◽  
Tensor Densities

We study noncommutative theory of a coadjoint representation of a universal extension of Vect (S1) ⋉ C∞(S1) algebra using the action of ⋆-deformed matrix Hill's operators Δ⋆ on the space of ⋆-deformed tensor densities. The centrally extended semidirect product algebra [Formula: see text] is a Lie algebra of extended semidirect product of the Bott–Virasoro group [Formula: see text]. The study of deformed diffeomorphisms, deformed semidirect product algebra and deformed Lie derivative action of Δ⋆ on ⋆ deformed tensor-densities on S1 allow us to construct noncommutative two component Korteweg–de Vries (KdV) equations, in particular, we derive the noncommutative Ito equation. This leads to a geometric formulation of ⋆-deformed quantization of the centrally extended semidirect product algebra [Formula: see text] and two component noncommutative KdV equations.

The Vacuum Distributions of the Truncated Virasoro Fields are Products of Gamma Distributions

2017 ◽  
Vol 24 (01) ◽  
pp. 1750004 ◽  
Author(s):  
Luigi Accardi ◽  
Andreas Boukas ◽  
Yun-Gang Lu
Keyword(s):  
Fourier Transform ◽  
Characteristic Function ◽  
Heisenberg Group ◽  
Lie Algebra ◽  
Fock Space ◽  
Random Variables ◽  
Virasoro Algebra ◽  
Commutation Relations ◽  
Gamma Distributions

In a recent paper, using a splitting formula for the multi-dimensional Heisenberg group, we derived a formula for the vacuum characteristic function (Fourier transform) of quantum random variables defined as self-adjoint sums of Fock space operators satisfying the multidimensional Heisenberg Lie algebra commutation relations. In this paper we use that formula to compute the characteristic function of quantum random variables defined as suitably truncated sums of the Virasoro algebra generators. By relating the structure of the Virasoro fields to the quadratic quantization program and using techniques developed in that context we prove that the vacuum distributions of the truncated Virasoro fields are products of independent, but not identically distributed, shifted Gamma-random variables.

INFINITE-DIMENSIONAL GENERALIZATIONS OF SIMPLE LIE ALGEBRAS

1990 ◽  
Vol 05 (24) ◽  
pp. 1967-1977 ◽  
Author(s):  
E. S. FRADKIN ◽  
V. YA. LINETSKY
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Virasoro Algebra ◽  
Simple Lie Algebras ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Higher Spin ◽  
Higher Spin Theory

Infinite-dimensional algebras associated with simple finite-dimensional Lie algebra g are considered. Higher-spin generalizations of sl(2) are studied in detail. Those of the Virasoro algebra are viewed as their "analytic continuations". Applications in higher-spin theory and in conformal QFT are discussed.

MODIFIED KORTEWEG-DE VRIES EQUATIONS ON EUCLIDEAN LIE ALGEBRAS

1989 ◽  
Vol 03 (06) ◽  
pp. 853-861 ◽  
Author(s):  
B.A. KUPERSHMIDT
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Virasoro Algebra ◽  
One Dimensional ◽  
Finite Dimensional ◽  
De Vries

For any finite-dimensional Euclidean Lie alegebra [Formula: see text], a commuting hierarchy of generalized modified Korteweg-de Vries equations is constructed, together with a nonabelian generalization of the classical Miura map. The classical situation is recovered for the case when [Formula: see text] is abelian one-dimensional. Localization of differential formulae yields a representation of the Virasoro algebra in terms of elements of the current Lie algebra associated to [Formula: see text].

Unitary representations of the Virasoro algebra

1986 ◽  
Vol 53 (4) ◽  
pp. 1013-1046 ◽  
Author(s):  
Akihiro Tsuchiya ◽  
Yukihiro Kanie
Keyword(s):  
Virasoro Algebra ◽  
Unitary Representations
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