Geodesic
COHOMOLOGY OF SPLIT ALGEBRAS AND OF TRIVIAL EXTENSIONS
Glasgow mathematical journal, Tome 45 (2003) no. 1, pp. 21-40

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DOI

We consider associative algebras $\Lambda$ 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 $\Lambda$. 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.
DOI : 10.1017/S0017089502008959
Mots-clés : 16E40, 16D20 
CIBILS, CLAUDE; MARCOS, EDUARDO; REDONDO, MARÍA JULIA; SOLOTAR, ANDREA. COHOMOLOGY OF SPLIT ALGEBRAS AND OF TRIVIAL EXTENSIONS. Glasgow mathematical journal, Tome 45 (2003) no. 1, pp. 21-40. doi: 10.1017/S0017089502008959
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     title = {COHOMOLOGY {OF} {SPLIT} {ALGEBRAS} {AND} {OF} {TRIVIAL} {EXTENSIONS}},
     journal = {Glasgow mathematical journal},
     pages = {21--40},
     year = {2003},
     volume = {45},
     number = {1},
     doi = {10.1017/S0017089502008959},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502008959/}
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