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JOSEPH IDEALS AND LISSE MINIMAL $W$-ALGEBRAS

Part of: Lie algebras and Lie superalgebras Groups and algebras in quantum theory

Published online by Cambridge University Press:  07 March 2016

Tomoyuki Arakawa  and
Anne Moreau
Tomoyuki Arakawa
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan (arakawa@kurims.kyoto-u.ac.jp)
Anne Moreau
Affiliation:
Laboratoire de Mathématiques et Applications, Téléport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France (anne.moreau@math.univ-poitiers.fr)
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Abstract

We consider a lifting of Joseph ideals for the minimal nilpotent orbit closure to the setting of affine Kac–Moody algebras and find new examples of affine vertex algebras whose associated varieties are minimal nilpotent orbit closures. As an application we obtain a new family of lisse ($C_{2}$-cofinite) $W$-algebras that are not coming from admissible representations of affine Kac–Moody algebras.

Keywords

Joseph idealassociated varietyDeligne exceptional seriesaffine Kac–Moody algebraaffine W-algebra

MSC classification

Primary: 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 17B69: Vertex operators; vertex operator algebras and related structures 81R10: Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 17 , Issue 2 , April 2018 , pp. 397 - 417
Copyright
© Cambridge University Press 2016 

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