Harish-Chandra Modules of the Intermediate Series over the Topological N = 2 Superconformal Algebra

2020 ◽  
Vol 27 (02) ◽  
pp. 343-360 ◽  
Author(s):  
Hengyun Yang ◽  
Ying Xu ◽  
Jiancai Sun
Keyword(s):  
Topological Strings ◽  
Symmetry Algebra ◽  
Lie Superalgebra ◽  
Superconformal Algebra ◽  
Infinite Dimensional ◽  
Graded Modules ◽  
Intermediate Series

The topological N = 2 superconformal algebra was introduced by Dijkgraaf, Verlinde and Verlinde as the symmetry algebra of topological strings at d < 1. We give a classification of irreducible 𝕫 × 𝕫-graded modules of the intermediate series over this infinite-dimensional Lie superalgebra.

Classification of Z-Graded Modules of the Intermediate Series over the q-Analog Virasoro-like Algebra

2010 ◽  
Vol 17 (02) ◽  
pp. 247-256
Author(s):  
Yina Wu ◽  
Weiqiang Lin
Keyword(s):  
Graded Modules ◽  
Direct Sum ◽  
Intermediate Series

In this paper, we complete the classification of Z-graded modules of the intermediate series over a q-analog Virasoro-like algebra L. We first construct four classes of irreducible Z-graded L-modules of the intermediate series. Then we prove that any Z-graded L-module of the intermediate series must be one of the modules constructed by us, or a direct sum of some trivial L-modules.

Classification of ℤ2-graded modules of intermediate series over a Block-type Lie algebra

2015 ◽  
Vol 17 (05) ◽  
pp. 1550059
Author(s):  
Yucai Su ◽  
Xiaoqing Yue
Keyword(s):  
Lie Algebra ◽  
Block Type ◽  
Graded Modules ◽  
Intermediate Series

Let [Formula: see text] be the Lie algebra of Block type with basis {Li,j | i,j ∈ ℤ} and relations [Li,j, Lk,l] = ((j + 1)k - (l + 1)i)Li+k,j+l. Since [Formula: see text] is ℤ2-graded, it is natural to study ℤ2-graded modules over [Formula: see text]. In this paper, ℤ2-graded [Formula: see text]-modules of the intermediate series are classified.

scholarly journals The classification of modular Lie superalgebras of type M

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Lili Ma ◽  
Liangyun Chen
Keyword(s):  
Intrinsic Property ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Characteristic P ◽  
Infinite Dimensional ◽  
Modular Lie Superalgebra ◽  
Nilpotent Elements ◽  
Natural Filtration ◽  
Modular Lie Superalgebras

AbstractThe natural filtration of the infinite-dimensional simple modular Lie superalgebra M over a field of characteristic p > 2 is proved to be invariant under automorphisms by discussing ad-nilpotent elements. Moreover, an intrinsic property is obtained and all the infinite-dimensional simple modular Lie superalgebras M are classified up to isomorphisms. As an application, a property of automorphisms of M is given.

Lie subgroups of symmetry groups of fluid dynamics and magnetohydro-dynamics equations

1995 ◽  
Vol 73 (7-8) ◽  
pp. 463-477 ◽  
Author(s):  
A. M. Grundland ◽  
L. Lalague
Keyword(s):  
Fluid Dynamics ◽  
Symmetry Algebra ◽  
Symmetry Groups ◽  
Systems Of Equations ◽  
Magnetohydrodynamics Equations ◽  
Infinite Dimensional ◽  
Isentropic Flow ◽  
Fluid Dynamics Equations ◽  
Symmetry Algebras

We classify the subalgebras of the symmetry algebras of fluid dynamics and magnetohydrodynamics equations into conjugacy classes under their respective groups. Both systems of equations are invariant under a Galilean-similitude algebra. In the case of the fluid dynamics equations, when the adiabatic exponent γ = 5/3, the symmetry algebra widens to a Galilean-projective algebra. We extend our previous classification of the symmetry algebra in the case of a nonstationary and isentropic flow to the general case of fluid dynamics and magnetohydrodynamics equations in (3 + 1) dimensions. The representatives of these algebras are given in normalized lists and presented in tables. Examples of invariant and partially invariant solutions, for both systems, are computed from representatives of these classifications. The final part of this work contains an analysis of this classification in connection with a further classification of the symmetry algebras in the case of the equations describing the flow of perfect gases. An explicit solution, in terms of Riemann invariants, is constructed from infinite-dimensional subalgebras of the symmetry algebra of the magnetohydrodynamics equations in the (1 + 2)-dimensional case.

Quasi-finite Irreducible Graded Modules for the Virasoro-like Algebra

2013 ◽  
Vol 20 (02) ◽  
pp. 181-196 ◽  
Author(s):  
Weiqiang Lin ◽  
Yucai Su
Keyword(s):  
Weight Module ◽  
Highest Weight Module ◽  
Graded Modules ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Irreducible Modules ◽  
Graded Module ◽  
Intermediate Series ◽  
Uniformly Bounded

In this paper, we consider the classification of irreducible Z- and Z2-graded modules with finite-dimensional homogeneous subspaces over the Virasoro-like algebra. We prove that such a module is a uniformly bounded module or a generalized highest weight module. Then we determine all generalized highest weight quasi-finite irreducible modules. As a consequence, we determine all the modules with nonzero center. Finally, we prove that there does not exist any non-trivial Z-graded module of intermediate series.

scholarly journals REPRESENTATIONS OF THE EXCEPTIONAL LIE SUPERALGEBRA E(3,6) III: CLASSIFICATION OF SINGULAR VECTORS

2005 ◽  
Vol 04 (01) ◽  
pp. 15-57 ◽  
Author(s):  
VICTOR G. KAC ◽  
ALEXEI RUDAKOV
Keyword(s):  
Vector Fields ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Irreducible Representations ◽  
Verma Modules ◽  
Locally Finite ◽  
Infinite Dimensional ◽  
Singular Vectors ◽  
Zero Degree

We continue the study of irreducible representations of the exceptional Lie superalgebra E(3,6). This is one of the two simple infinite-dimensional Lie superalgebras of vector fields which have a Lie algebra sℓ(3) × sℓ(2) × gℓ(1) as the zero degree component of its consistent ℤ-grading. We provide the classification of the singular vectors in the degenerate Verma modules over E(3,6), completing thereby the classification and construction of all irreducible E(3,6)-modules that are L0-locally finite.

scholarly journals Classification of Degenerate Verma Modules for E(5, 10)

2021 ◽  
Author(s):  
Nicoletta Cantarini ◽  
Fabrizio Caselli ◽  
Victor Kac
Keyword(s):  
Infinite Number ◽  
Verma Module ◽  
Lie Superalgebra ◽  
Verma Modules ◽  
Singular Vectors ◽  
Finite Dimensional ◽  
De Rham ◽  
Via Classification

AbstractGiven a Lie superalgebra $${\mathfrak {g}}$$ g with a subalgebra $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 , and a finite-dimensional irreducible $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 -module F, the induced $${\mathfrak {g}}$$ g -module $$M(F)={\mathcal {U}}({\mathfrak {g}})\otimes _{{\mathcal {U}}({\mathfrak {g}}_{\ge 0})}F$$ M ( F ) = U ( g ) ⊗ U ( g ≥ 0 ) F is called a finite Verma module. In the present paper we classify the non-irreducible finite Verma modules over the largest exceptional linearly compact Lie superalgebra $${\mathfrak {g}}=E(5,10)$$ g = E ( 5 , 10 ) with the subalgebra $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 of minimal codimension. This is done via classification of all singular vectors in the modules M(F). Besides known singular vectors of degree 1,2,3,4 and 5, we discover two new singular vectors, of degrees 7 and 11. We show that the corresponding morphisms of finite Verma modules of degree 1,4,7, and 11 can be arranged in an infinite number of bilateral infinite complexes, which may be viewed as “exceptional” de Rham complexes for E(5, 10).

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