scholarly journals A Classification of Indecomposable sl2(C)-Modules and a Conjecture of Kac on Irreducible Modules over the Virasoro Algebra

1993 ◽  
Vol 161 (1) ◽  
pp. 33-46 ◽  
Author(s):  
Y.C. Su
Keyword(s):  
Virasoro Algebra ◽  
Irreducible Modules

scholarly journals Classification of irreducible Harish-Chandra modules over generalized Virasoro algebras

2012 ◽  
Vol 55 (3) ◽  
pp. 697-709 ◽  
Author(s):  
Xiangqian Guo ◽  
Rencai Lu ◽  
Kaiming Zhao
Keyword(s):  
Direct Summand ◽  
Virasoro Algebra ◽  
Additive Subgroup ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Irreducible Modules ◽  
Intermediate Series ◽  
Complex Number Field ◽  
Weight Modules

AbstractLet G be an arbitrary non-zero additive subgroup of the complex number field ℂ, and let Vir[G] be the corresponding generalized Virasoro algebra over ℂ. In this paper we determine all irreducible weight modules with finite-dimensional weight spaces over Vir[G]. The classification strongly depends on the index group G. If G does not have a direct summand isomorphic to ℤ (the integers), then such irreducible modules over Vir[G] are only modules of intermediate series whose weight spaces are all one dimensional. Otherwise, there is one further class of modules that are constructed by using intermediate series modules over a generalized Virasoro subalgebra Vir[G0] of Vir[G] for a direct summand G0 of G with G = G0 ⊕ ℤb, where b ∈ G \ G0. This class of irreducible weight modules do not have corresponding weight modules for the classical Virasoro algebra.

scholarly journals CLASSIFICATION OF GRADED LEFT-SYMMETRIC ALGEBRAIC STRUCTURES ON WITT AND VIRASORO ALGEBRAS

2011 ◽  
Vol 22 (02) ◽  
pp. 201-222 ◽  
Author(s):  
XIAOLI KONG ◽  
HONGJIA CHEN ◽  
CHENGMING BAI
Keyword(s):  
Virasoro Algebra ◽  
Indecomposable Module ◽  
Multiplication Operators ◽  
Algebraic Structures ◽  
Witt Algebra ◽  
Left Multiplication ◽  
Symmetric Algebras ◽  
Nonlinear Math ◽  
Math Phys

We find that a compatible graded left-symmetric algebraic structure on the Witt algebra induces an indecomposable module V of the Witt algebra with one-dimensional weight spaces by its left-multiplication operators. From the classification of such modules of the Witt algebra, the compatible graded left-symmetric algebraic structures on the Witt algebra are classified. All of them are simple and they include the examples given by [Comm. Algebra32 (2004) 243–251; J. Nonlinear Math. Phys.6 (1999) 222–245]. Furthermore, we classify the central extensions of these graded left-symmetric algebras which give the compatible graded left-symmetric algebraic structures on the Virasoro algebra. They coincide with the examples given by [J. Nonlinear Math. Phys.6 (1999) 222–245].

scholarly journals Classification of Finite Irreducible Modules over the Lie Conformal Superalgebra CK 6

2012 ◽  
Vol 317 (2) ◽  
pp. 503-546 ◽  
Author(s):  
Carina Boyallian ◽  
Victor G. Kac ◽  
José I. Liberati
Keyword(s):  
Irreducible Modules

scholarly journals Unitary Modules for the Twisted Heisenberg–Virasoro Algebra

2019 ◽  
Vol 26 (03) ◽  
pp. 529-540
Author(s):  
Xiufu Zhang ◽  
Shaobin Tan ◽  
Haifeng Lian
Keyword(s):  
Virasoro Algebra ◽  
Irreducible Module ◽  
Irreducible Modules ◽  
Intermediate Series

The conjugate-linear anti-involutions and unitary irreducible modules of the intermediate series over the twisted Heisenberg–Virasoro algebra are classified, respectively. We prove that any unitary irreducible module of the intermediate series over the twisted Heisenberg–Virasoro algebra is of the form [Formula: see text] for [Formula: see text], [Formula: see text] and [Formula: see text].

scholarly journals Classification of Irreducible Modules for the Vertex Operator AlgebraM(1)+

1999 ◽  
Vol 216 (1) ◽  
pp. 384-404 ◽  
Author(s):  
Chongying Dong ◽  
Kiyokazu Nagatomo
Keyword(s):  
Vertex Operator ◽  
Irreducible Modules

scholarly journals HIGHEST WEIGHT REPRESENTATIONS AND KAC DETERMINANTS FOR A CLASS OF CONFORMAL GALILEI ALGEBRAS WITH CENTRAL EXTENSION

2012 ◽  
Vol 23 (11) ◽  
pp. 1250118 ◽  
Author(s):  
NARUHIKO AIZAWA ◽  
PHILLIP S. ISAAC ◽  
YUTA KIMURA
Keyword(s):  
Central Extension ◽  
Spatial Dimension ◽  
Verma Modules ◽  
Infinite Dimensional ◽  
Singular Vectors ◽  
Highest Weight ◽  
Irreducible Modules ◽  
Highest Weight Representations ◽  
Quotient Modules

We investigate the representations of a class of conformal Galilei algebras in one spatial dimension with central extension. This is done by explicitly constructing all singular vectors within the Verma modules, proving their completeness and then deducing irreducibility of the associated highest weight quotient modules. A resulting classification of infinite dimensional irreducible modules is presented. It is also shown that a formula for the Kac determinant is deduced from our construction of singular vectors. Thus we prove a conjecture of Dobrev, Doebner and Mrugalla for the case of the Schrödinger algebra.

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