$\mathcal{W}(a,b)$ Lie Conformal Algebra and Its Conformal Module of Rank One

DOI10.1142/S1005386715000358zbMath1394.17056WikidataQ115244727 ScholiaQ115244727MaRDI QIDQ2949733

Xiao Qing Yue, Ying Xu

Publication date: 2 October 2015

Published in: Algebra Colloquium (Search for Journal in Brave)

zbMATH Keywords

Virasoro algebraLie conformal algebrasmodules over Lie conformal algebras\(\mathcal{W}(a,b)\) algebraformal distribution Lie algebras

Mathematics Subject Classification ID

Virasoro and related algebras (17B68) Vertex operators; vertex operator algebras and related structures (17B69)

Related Items (11)

Lie conformal algebras of planar Galilean type ⋮ Structures of \(W(2,2)\) Lie conformal algebra ⋮ The Heisenberg-Virasoro Lie conformal superalgebra ⋮ Extensions of finite irreducible modules of Lie conformal algebras W(a,b) and some Schrödinger-Virasoro type Lie conformal algebras ⋮ Unnamed Item ⋮ Classification of finite irreducible conformal modules over some Lie conformal algebras related to the Virasoro conformal algebra ⋮ Classification of finite irreducible conformal modules over Lie conformal algebra \(\mathcal{W}(a,b,r)\) ⋮ Loop W(a,b) Lie conformal algebra ⋮ Finite irreducible modules of Lie conformal algebras 𝒲(a,b) and some Schrödinger–Virasoro type Lie conformal algebras ⋮ Infinite rank Schrödinger-Virasoro type Lie conformal algebras ⋮ Extensions of modules over a class of Lie conformal algebras 𝒲(b)

Cites Work

• \(W\)-algebra \(W\)(2, 2) and the vertex operator algebra \({L(\frac{1}{2},\,0)\,\otimes\, L(\frac{1}{2},\,0)}\)
• Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac
• Classification of Harish-Chandra modules over the Virasoro Lie algebra
• Cohomology of conformal algebras
• Conformal modules
• A classification of indecomposable \(sl_ 2(\mathbb{C})\)-modules and a conjecture of Kac on irreducible modules over the Virasoro algebra
• Classification of Harish-Chandra modules over the higher rank Virasoro algebras
• Classification of finite simple Lie conformal superalgebras.
• Classification of quasifinite modules over the Lie algebras of Weyl type.
• CLASSIFICATION OF INFINITE DIMENSIONAL WEIGHT MODULES OVER THE LIE SUPERALGEBRAsl(2/1)
• CLASSIFICATION OF IRREDUCIBLE WEIGHT MODULES OVER THE TWISTED HEISENBERG–VIRASORO ALGEBRA
• Low dimensional cohomology of general conformal algebras gcN
• Classification of indecomposable modules of the intermediate series over the twisted N=2 superconformal algebra
• Representations of the Schrödinger–Virasoro algebras
• Theory of finite pseudoalgebras

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