## On almost nilpotent varieties of subexponential growth.(English)Zbl 1333.17001

Summary: Let $${}_2\mathcal{N}$$ be the variety of left-nilpotent algebras of index two, that is the variety of algebras satisfying the identity $$x(y z) \equiv 0$$. We introduce two new varieties, denoted by $$\mathcal{V}_{\mathit{sym}}$$ and $$\mathcal{V}_{\mathit{alt}}$$, contained in the variety $${}_2\mathcal{N}$$ and we prove that $$\mathcal{V}_{\mathit{sym}}$$ and $$\mathcal{V}_{\mathit{alt}}$$ are the only two varieties almost nilpotent of subexponential growth.

### MSC:

 17A30 Nonassociative algebras satisfying other identities

### Keywords:

polynomial identity; variety; almost nilpotent; codimension
Full Text:

### References:

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