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 |
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paper:paper_00170895_v45_n1_p21_Cibils2023-06-08T14:39:00Z 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 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. 2003 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 |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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. |
| title |
Cohomology of split algebras and of trivial extensions |
| spellingShingle |
Cohomology of split algebras and of trivial extensions |
| title_short |
Cohomology of split algebras and of trivial extensions |
| title_full |
Cohomology of split algebras and of trivial extensions |
| title_fullStr |
Cohomology of split algebras and of trivial extensions |
| title_full_unstemmed |
Cohomology of split algebras and of trivial extensions |
| title_sort |
cohomology of split algebras and of trivial extensions |
| publishDate |
2003 |
| url |
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 |
| _version_ |
1768544210506481664 |