Infinitely dimensional, affine nil algebras $A\otimes A^{op}$ and $A\otimes A$ exist

preprint2014arXivOpen access

In this paper we answer two questions from [16], by showing that, over any algebraically closed field, $K$ , there is a finitely generated, infinitely dimensional algebra $A$ such that algebras $A\otimes_{K}A$ and $A\otimes_{K} A^{op}$ are nil.

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Infinitely dimensional, affine nil algebras $A\otimes A^{op}$ and $A\otimes A$ exist

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Infinitely dimensional, affine nil algebras A⊗AopA\otimes A^{op}A⊗Aop and A⊗AA\otimes AA⊗A exist

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Infinitely dimensional, affine nil algebras $A\otimes A^{op}$ and $A\otimes A$ exist