2017/12/15 by Xiao He, He, Xiao
Mathematics · #17B56 #17B70 #17B81 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1712.05484
openalex publication_date 2017/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.