Cohomology of split algebras and of trivial extensions
We consider associative algebras λ over a field provided with a direct sum decomposition of a two-sided ideal M and a sub-algebra A - examples are provided by trivial extensions or triangular type matrix algebras. In this relative and split setting we describe a long exact sequence computing the Hoc...
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2003
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00170895_v45_n1_p21_Cibils http://hdl.handle.net/20.500.12110/paper_00170895_v45_n1_p21_Cibils |
| Aporte de: |
| Sumario: | We consider associative algebras λ over a field provided with a direct sum decomposition of a two-sided ideal M and a sub-algebra A - examples are provided by trivial extensions or triangular type matrix algebras. In this relative and split setting we describe a long exact sequence computing the Hochschild cohomology of λ. We study the connecting homomorphism using the cup-product and we infer several results, in particular the first Hochschild cohomology group of a trivial extension never vanishes. |
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