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Given a nonsemisimple symmetric algebra B and a non-selfinjective algebra A (all algebras are finite dimensional over a field and connected). Can A and B have isomorphic Hochschild-cohomology rings?

Given a nonsemisimple symmetric algebra B and a non-selfinjective algebra A (all algebras are finite dimensional over a field). Can A and B have isomorphic Hochschild-cohomology rings?

Given a nonsemisimple symmetric algebra B and a non-selfinjective algebra A (all algebras are finite dimensional over a field and connected). Can A and B have isomorphic Hochschild-cohomology rings?

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Mare
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  • 104

A question on Hochschild cohomology

Given a nonsemisimple symmetric algebra B and a non-selfinjective algebra A (all algebras are finite dimensional over a field). Can A and B have isomorphic Hochschild-cohomology rings?