Classification of indecomposable modules of the intermediate series over the twisted N=2 superconformal algebra

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.

Download Full-text

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

Algebra Colloquium ◽

10.1142/s100538671000026x ◽

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.

Download Full-text

Classification of irreducible Harish-Chandra modules over generalized Virasoro algebras

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091510001604 ◽

2012 ◽

Vol 55 (3) ◽

pp. 697-709 ◽

Cited By ~ 4

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.

Download Full-text

Indecomposable modules of the intermediate series over W(a, b)

Science China Mathematics ◽

10.1007/s11425-013-4630-0 ◽

2013 ◽

Vol 57 (2) ◽

pp. 275-291 ◽

Cited By ~ 3

Author(s):

YuCai Su ◽

Ying Xu ◽

XiaoQing Yue

Keyword(s):

Indecomposable Modules ◽

Intermediate Series

Download Full-text

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

Communications in Contemporary Mathematics ◽

10.1142/s0219199715500595 ◽

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.

Download Full-text

Classification of linked indecomposable modules of a family of solvable Lie algebras over an arbitrary field of characteristic 0

Journal of Algebra and Its Applications ◽

10.1142/s0219498816500298 ◽

2015 ◽

Vol 15 (02) ◽

pp. 1650029 ◽

Cited By ~ 1

Author(s):

Leandro Cagliero ◽

Fernando Szechtman

Keyword(s):

Lie Algebra ◽

Lie Algebras ◽

Weight Space ◽

Arbitrary Field ◽

Nilpotent Radical ◽

Indecomposable Modules ◽

Finite Dimensional ◽

A Chain ◽

Algebra Over A Field

Let 𝔤 be a finite-dimensional Lie algebra over a field of characteristic 0, with solvable radical 𝔯 and nilpotent radical 𝔫 = [𝔤, 𝔯]. Given a finite-dimensional 𝔤-module U, its nilpotency series 0 ⊂ U(1) ⊂ ⋯ ⊂ U(m) = U is defined so that U(1) is the 0-weight space of 𝔫 in U, U(2)/U(1) is the 0-weight space of 𝔫 in U/U(1), and so on. We say that U is linked if each factor of its nilpotency series is a uniserial 𝔤/𝔫-module, i.e. its 𝔤/𝔫-submodules form a chain. Every uniserial 𝔤-module is linked, every linked 𝔤-module is indecomposable with irreducible socle, and both converses fail. In this paper, we classify all linked 𝔤-modules when 𝔤 = 〈x〉 ⋉ 𝔞 and ad x acts diagonalizably on the abelian Lie algebra 𝔞. Moreover, we identify and classify all uniserial 𝔤-modules amongst them.

Download Full-text