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Suppose $(A, (\mu_k))$ is a (curved) $A_\infty$ algebra, and let $(\tilde A, (\tilde\mu_k))$ be its minimal model. Now, we have two Hochschild cohomology rings $HH^*(A)$ and $HH^*(\tilde A)$. (It may be also related to $HH^*(A,\tilde A)$ or $HH^*(\tilde A,A)$ for the diagonal $A_\infty$ bimodules.)

Are there any natural relations between $HH^*(A)$ and $HH^*(\tilde A)$ ? What I'm interested most is the following question:

Question: Does there exist a ring homomorphism between them? (Any reference would be greatly appreciated.)

The ring structure is defined by $f\cdot g= \pm\mu(\cdots f(\cdots)\cdots g(\cdots) \cdots)$

Suppose $(A, (\mu_k))$ is a (curved) $A_\infty$ algebra, and let $(\tilde A, (\tilde\mu_k))$ be its minimal model. Now, we have two Hochschild cohomology rings $HH^*(A)$ and $HH^*(\tilde A)$. (It may be also related to $HH^*(A,\tilde A)$ or $HH^*(\tilde A,A)$ for the diagonal $A_\infty$ bimodules.)

Are there any natural relations between $HH^*(A)$ and $HH^*(\tilde A)$ ? What I'm interested most is the following question:

Question: Does there exist a natural ring homomorphism between them? (Any reference would be greatly appreciated.)

The ring structure is defined by $f\cdot g= \pm\mu(\cdots f(\cdots)\cdots g(\cdots) \cdots)$

Suppose $(A, (\mu_k))$ is a (curved) $A_\infty$ algebra, and let $(\tilde A, (\tilde\mu_k))$ be its minimal model. Now, we have two Hochschild cohomology rings $HH^*(A)$ and $HH^*(\tilde A)$. (It may be also related to $HH^*(A,\tilde A)$ or $HH^*(\tilde A,A)$ for the diagonal $A_\infty$ bimodules.)

Are there any natural relations between $HH^*(A)$ and $HH^*(\tilde A)$ ? What I'm interested most is the following question:

Question: Does there exist a ring homomorphism between them? (Any reference would be greatly appreciated.)

Suppose $(A, (\mu_k))$ is a (curved) $A_\infty$ algebra, and let $(\tilde A, (\tilde\mu_k))$ be its minimal model. Now, we have two Hochschild cohomology rings $HH^*(A)$ and $HH^*(\tilde A)$. (It may be also related to $HH^*(A,\tilde A)$ or $HH^*(\tilde A,A)$ for the diagonal $A_\infty$ bimodules.)

Are there any natural relations between $HH^*(A)$ and $HH^*(\tilde A)$ ? What I'm interested most is the following question:

Question: Does there exist a ring homomorphism between them? (Any reference would be greatly appreciated.)

The ring structure is defined by $f\cdot g= \pm\mu(\cdots f(\cdots)\cdots g(\cdots) \cdots)$

Suppose $(A, (\mu_k))$ is a (curved) $A_\infty$ algebra, and let $(\tilde A, (\tilde\mu_k))$ be its minimal model. Now, we have two Hochschild cohomology rings $HH^*(A)$ and $HH^*(\tilde A)$. (It may be also related to $HH^*(A,\tilde A)$ or $HH^*(\tilde A,A)$ for the diagonal $A_\infty$ bimodules.)

Question: Are there any natural relations between $HH^*(A)$ and $HH^*(\tilde A)$ ? For instance, does there exist a ring homomorphism between them? Any reference would be greatly appreciated.

Suppose $(A, (\mu_k))$ is a (curved) $A_\infty$ algebra, and let $(\tilde A, (\tilde\mu_k))$ be its minimal model. Now, we have two Hochschild cohomology rings $HH^*(A)$ and $HH^*(\tilde A)$. (It may be also related to $HH^*(A,\tilde A)$ or $HH^*(\tilde A,A)$ for the diagonal $A_\infty$ bimodules.)

Are there any natural relations between $HH^*(A)$ and $HH^*(\tilde A)$ ? What I'm interested most is the following question:

Question: Does there exist a ring homomorphism between them? (Any reference would be greatly appreciated.)