Lower-estimates on the hochschild (Co)homological dimension of commutative algebras and applications to smooth affine schemes and quasi-free algebras
- Journal Article
Rights / licenseCreative Commons Attribution 4.0 International
The Hochschild cohomological dimension of any commutative k-algebra is lower-bounded by the least-upper bound of the flat-dimension difference and its global dimension. Our result is used to show that for a smooth affine scheme X satisfying Pointcaré duality, there must exist a vector bundle with section M and suitable n which the module of algebraic differential n-forms Ωn(X,M). Further restricting the notion of smoothness, we use our result to show that most k-algebras fail to be smooth in the quasi-free sense. This consequence, extends the currently known results, which are restricted to the case where k=C. Show more
Journal / seriesMathematics
Pages / Article No.
Subjecthochschild cohomology; homological dimension theory; non-commutative geometry; quasi-free algebras; pointcaré duality; higher differential forms
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