Abstract We first prove that a left Novikov algebra is right nilpotent if and only if it is solvable. Then we show that, every Novikov algebra that can be represented as the sum of two solvable subalgebras is itself solvable, moreover, if the two solvable subalgebras are abelian, then the whole algebra is metabelian. Finally, we show that for every every n-generated non-abelian free solvable (or non-abelian free right nilpotent) Novikov algebra has wild automorphisms.

中文翻译：

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诺维科夫代数的可解性和幂零性

摘要 我们首先证明左诺维科夫代数是右幂零当且仅当它是可解的。然后我们证明，每一个可以表示为两个可解子代数之和的诺维科夫代数本身都是可解的，而且，如果这两个可解子代数是阿贝尔代数，那么整个代数都是元贝尔代数。最后，我们证明对于每一个 n 生成的非阿贝尔自由可解（或非阿贝尔自由右幂零）诺维科夫代数都具有野生自同构。