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JOSEPH IDEALS AND LISSE MINIMAL $W$ -ALGEBRAS

Published online by Cambridge University Press:  07 March 2016

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)

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.

Type
Research Article
Copyright
© Cambridge University Press 2016 

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