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The universal envelooeenvelope U(L) is a PI-algebra iff L is abelian

Question:

k isLet $k$ be a field with char k = 0$\operatorname{char} k = 0$. L isLet $L$ be a Lie k$k$-algebra, then. Then the universal envelooe U(L)envelope $U(L)$ is a PI-algebra iff L$L$ is abelian.

Remark: PI-algebra means polynomial identity algebra, an algebra that satisfies a nonzero polynomial.

Obviously, if L$L$ is abelian, then U(L)$U(L)$ is commutative. But the reverse direction is difficult for me. I also know that this is a result in an article "Two remarks on PI-algebras, V.N.Latysev". But I can not find the article.

The universal envelooe U(L) is a PI-algebra iff L is abelian

Question:

k is a field with char k = 0. L is a Lie k-algebra, then the universal envelooe U(L) is a PI-algebra iff L is abelian.

Remark: PI-algebra means polynomial identity algebra, an algebra that satisfies a nonzero polynomial.

Obviously, if L is abelian, then U(L) is commutative. But the reverse direction is difficult for me. I also know that this is a result in an article "Two remarks on PI-algebras, V.N.Latysev". But I can not find the article.

The universal envelope U(L) is a PI-algebra iff L is abelian

Let $k$ be a field with $\operatorname{char} k = 0$. Let $L$ be a Lie $k$-algebra. Then the universal envelope $U(L)$ is a PI-algebra iff $L$ is abelian.

Remark: PI-algebra means polynomial identity algebra, an algebra that satisfies a nonzero polynomial.

Obviously, if $L$ is abelian, then $U(L)$ is commutative. But the reverse direction is difficult for me. I also know that this is a result in an article "Two remarks on PI-algebras, V.N.Latysev". But I can not find the article.

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The universal envelooe U(L) is a PI-algebra iff L is abelian

Question:

k is a field with char k = 0. L is a Lie k-algebra, then the universal envelooe U(L) is a PI-algebra iff L is abelian.

Remark: PI-algebra means polynomial identity algebra, an algebra that satisfies a nonzero polynomial.

Obviously, if L is abelian, then U(L) is commutative. But the reverse direction is difficult for me. I also know that this is a result in an article "Two remarks on PI-algebras, V.N.Latysev". But I can not find the article.