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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Autores principales: Cibils, C., Marcos, E., Redondo, M.J., Solotar, A.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00170895_v45_n1_p21_Cibils
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00170895_v45_n1_p21_Cibils2023-10-03T14:14:56Z Cohomology of split algebras and of trivial extensions Cibils, C. Marcos, E. Redondo, M.J. Solotar, A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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.
format JOUR
author Cibils, C.
Marcos, E.
Redondo, M.J.
Solotar, A.
spellingShingle Cibils, C.
Marcos, E.
Redondo, M.J.
Solotar, A.
Cohomology of split algebras and of trivial extensions
author_facet Cibils, C.
Marcos, E.
Redondo, M.J.
Solotar, A.
author_sort Cibils, C.
title 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
url http://hdl.handle.net/20.500.12110/paper_00170895_v45_n1_p21_Cibils
work_keys_str_mv AT cibilsc cohomologyofsplitalgebrasandoftrivialextensions
AT marcose cohomologyofsplitalgebrasandoftrivialextensions
AT redondomj cohomologyofsplitalgebrasandoftrivialextensions
AT solotara cohomologyofsplitalgebrasandoftrivialextensions
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