We introduce and investigate the properties of Hochschild cohomology of algebras in an abelian monoidal category M. We show that the second Hochschild cohomology group of an algebra in M classifies extensions of A up to an equivalence. We characterize algebras of Hochschild dimension 0 (separable algebras), and of Hochschild dimension less or equal to 1 (formally smooth algebras). Several particular cases and applications are included in the last section of the paper.
Hochschild Cohomology And 'Smoothness' In Monoidal Categories
ARDIZZONI, Alessandro;
2007-01-01
Abstract
We introduce and investigate the properties of Hochschild cohomology of algebras in an abelian monoidal category M. We show that the second Hochschild cohomology group of an algebra in M classifies extensions of A up to an equivalence. We characterize algebras of Hochschild dimension 0 (separable algebras), and of Hochschild dimension less or equal to 1 (formally smooth algebras). Several particular cases and applications are included in the last section of the paper.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
03-HochschildCohom.pdf
Accesso riservato
Tipo di file:
PDF EDITORIALE
Dimensione
1.36 MB
Formato
Adobe PDF
|
1.36 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
