We study codimension growth of infinite dimensional Lie algebras over a fieldof characteristic zero. We prove that if a Lie algebra $L$ is an extension of anilpotent algebra by a finite dimensional semisimple algebra then thePI-exponent of $L$ exists and is a positive integer.
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机译：我们研究特征零域上的无限维李代数的共维增长。我们证明，如果李代数$ L $是有限幂半简单代数对幂等代数的扩展，则$ L $的PI指数存在且为正整数。
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