Hochschild Cohomological Dimension is Not Upper Semi-Continuous
Abstract
It is shown that the Hochschild Cohomological dimension of an associative algebra is not an upper-semi continuous function, showing the semi-continuity theorem is no longer valid for non-commutative algebras. A family of C exhibits this-algebras parameterized by C all but one of which has Hochschild cohomological dimension 2 and the other having Hochschild cohomological dimension 1.
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