On the Extended W-Algebra of Type sl2 at Positive Rational Level

Akihiro Tsuchiya; Simon Wood

doi:10.1093/imrn/rnu090

On the Extended W-Algebra of Type sl₂ at Positive Rational Level

Akihiro Tsuchiya, Simon Wood^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

The extended W-algebra of type sl₂ at positive rational level, denoted byM_p+,p-, is a vertex operator algebra (VOA) that was originally proposed in [16]. This VOA is an extension of the minimal model VOA and plays the role of symmetry algebra for certain logarithmic conformal field theories. We give a construction of M_p+,p- in terms of screening operators and use this construction to prove that M_p+,p- satisfies Zhu's c₂-cofiniteness condition, calculate the structure of the zero mode algebra (also known as Zhu's algebra), and classify all simpleM_p+,p--modules.

Original language	English
Pages (from-to)	5357-5435
Number of pages	79
Journal	International Mathematics Research Notices
Volume	2015
Issue number	14
DOIs	https://doi.org/10.1093/imrn/rnu090
Publication status	Published - 2015
Externally published	Yes

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abstract = "The extended W-algebra of type sl2 at positive rational level, denoted byMp+,p-, is a vertex operator algebra (VOA) that was originally proposed in [16]. This VOA is an extension of the minimal model VOA and plays the role of symmetry algebra for certain logarithmic conformal field theories. We give a construction of Mp+,p- in terms of screening operators and use this construction to prove that Mp+,p- satisfies Zhu's c2-cofiniteness condition, calculate the structure of the zero mode algebra (also known as Zhu's algebra), and classify all simpleMp+,p--modules.",

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AB - The extended W-algebra of type sl2 at positive rational level, denoted byMp+,p-, is a vertex operator algebra (VOA) that was originally proposed in [16]. This VOA is an extension of the minimal model VOA and plays the role of symmetry algebra for certain logarithmic conformal field theories. We give a construction of Mp+,p- in terms of screening operators and use this construction to prove that Mp+,p- satisfies Zhu's c2-cofiniteness condition, calculate the structure of the zero mode algebra (also known as Zhu's algebra), and classify all simpleMp+,p--modules.

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On the Extended W-Algebra of Type sl₂ at Positive Rational Level

Abstract

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