Prepublication:
Cohomology of split algebras and of trivial extensions

C. Cibils 
E. Marcos 
M.J. Redondo
A. Solotar

		
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.

http://www.math.univ-montp2.fr/~cibils/cmrs.html

http://xxx.lpthe.jussieu.fr/abs/math.KT/0102194