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arXiv · 1712.05484

A remark on semi-infinite cohomology

Xiao He
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Abstract

We extend the notion of semi-infinite cohomology of Lie algebras to include cases where the Lie algebra does not admit a semi-infinite structure but satisfies a mild condition. Our construction clarifies the definition of affine W-algebras in general nilpotent elements case given by V. Kac, S. Roan and M. Wakimoto. We will also give a characterization of admissible pairs with respect to a nilpotent element in a semisimple Lie algebra and define affine W-algebras associated to admissible pairs, while finite W-algebras associated to admissible pairs were already introduced before.

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Xiao He. 2017-12-15. A remark on semi-infinite cohomology. https://arxiv.org/abs/1712.05484

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