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joseph ideal

Journal of the Institute of Mathematics of Jussieu (1)

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JOSEPH IDEALS AND LISSE MINIMAL $W$-ALGEBRAS
Part of
- Lie algebras and Lie superalgebras
- Groups and algebras in quantum theory
Tomoyuki Arakawa, Anne Moreau
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 17 / Issue 2 / April 2018

Published online by Cambridge University Press:

07 March 2016, pp. 397-417

Print publication:

April 2018
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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.