On axiomatic approaches to vertex operator algebras and modules

Frenkel, Igor; Huang, Yi‐Zhi; Lepowsky, James

doi:10.1090/memo/0494

Cited by 613 publications

(674 citation statements)

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“…Proposition 2.6 ( [FHL,K2]). -Any vertex algebra V satisfies the following associativity property: for any A, B, C ∈ V we have the equality in V ((w))((z − w))…”

Section: The Meaning Of Localitymentioning

confidence: 99%

Vertex Algebras and Algebraic Curves

Frenkel

Ben‐Zvi

2004

Mathematical Surveys and Monographs

499

881

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“…Proposition 2.6 ( [FHL,K2]). -Any vertex algebra V satisfies the following associativity property: for any A, B, C ∈ V we have the equality in V ((w))((z − w))…”

Section: The Meaning Of Localitymentioning

confidence: 99%

Vertex Algebras and Algebraic Curves

Frenkel

Ben‐Zvi

2004

Mathematical Surveys and Monographs

499

881

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“…Let L p + ,p − be the lattice vertex-operator algebra (see [41,42,43]) generated by the vertex operators…”

Section: The Lattice Vertex-operator Algebramentioning

confidence: 99%

Logarithmic extensions of minimal models: Characters and modular transformations

et al. 2006

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ABSTRACT. We study logarithmic conformal field models that extend the (p, q) Virasoro minimal models. For coprime positive integers p and q, the model is defined as the kernel of the two minimal-model screening operators. We identify the field content, construct the W -algebra W p,q that is the model symmetry (the maximal local algebra in the kernel), describe its irreducible modules, and find their characters. We then derive the SL(2, Z)-representation on the space of torus amplitudes and study its properties. From the action of the screenings, we also identify the quantum group that is Kazhdan-Lusztig-dual to the logarithmic model. CONTENTS

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“…In some cases we can easily construct a linear operator T ∈ End(V ) satisfying (6), (7). This yields many examples of Lie algebras g T admitting a Novikov structure: Lemma 3.5.…”

Section: Construction Of Novikov Structures Via Classical R-matricesmentioning

confidence: 99%

“…Let g = sl 2 (C). Assume that T satisfies (6), (7). Then g T is isomorphic to one of the following Lie algebras: C 3 , n 3 (C) or r 3,−1 (C).…”

Section: Construction Of Novikov Structures Via Classical R-matricesmentioning

confidence: 99%

Novikov structures on solvable Lie algebras

Burde

Dekimpe

2006

Journal of Geometry and Physics

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Abstract. We study Novikov algebras and Novikov structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov structure must be solvable. Conversely we present an example of a nilpotent 2-step solvable Lie algebra without any Novikov structure. We construct Novikov structures on certain Lie algebras via classical r-matrices and via extensions. In the latter case we lift Novikov structures on an abelian Lie algebra a and a Lie algebra b to certain extensions of b by a. We apply this to prove the existence of affine and Novikov structures on several classes of 2-step solvable Lie algebras. In particular we generalize a well known result of Scheuneman concerning affine structures on 3-step nilpotent Lie algebras.

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On axiomatic approaches to vertex operator algebras and modules

Cited by 613 publications

References 0 publications

Vertex Algebras and Algebraic Curves

Vertex Algebras and Algebraic Curves

Logarithmic extensions of minimal models: Characters and modular transformations

Novikov structures on solvable Lie algebras

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