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並前往https://mathoverflow.net/questions/37101/computing-the-index-of-a-lie-algebra-what-is-known-beyond-the-reductive-case

Computing the index of a Lie algebra: what is known beyond ...

The following paper of M. Rais has a formula for index of semi-direct products that you mentioned. M. Rais "L'indice des produits semi-directs g⋉E. C. R. ...

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