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Francesco Polizzi
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Let $A$ be an $E_1$-algebra in chain complexes over $\mathbb Q$. Is there an easy way to check if $A$ admits the structure of an $E_2$-algebra (or $E_\infty$-algebra)?

Is there an easy way to check if $A$ admits the structure of an $E_2$-algebra (or $E_\infty$-algebra)?

Let $A$ be an $E_1$-algebra in chain complexes over $\mathbb Q$. Is there an easy way to check if $A$ admits the structure of an $E_2$-algebra (or $E_\infty$-algebra)?

Let $A$ be an $E_1$-algebra in chain complexes over $\mathbb Q$.

Is there an easy way to check if $A$ admits the structure of an $E_2$-algebra (or $E_\infty$-algebra)?

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Obstructions to $E_2$-algebra structure on $E_1$-algebra

Let $A$ be an $E_1$-algebra in chain complexes over $\mathbb Q$. Is there an easy way to check if $A$ admits the structure of an $E_2$-algebra (or $E_\infty$-algebra)?