Hochschild cohomology of relation extension algebras
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文摘
Let B be the split extension of a finite dimensional algebra C by a C-C-bimodule E  . We define a morphism of associative graded algebras φ:HH(B)→HH(C) from the Hochschild cohomology of B to that of C, extending similar constructions for the first cohomology groups made and studied by Assem, Bustamante, Igusa, Redondo and Schiffler.

In the case of a trivial extension B=C⋉E, we give necessary and sufficient conditions for each e506af14f07d1da69bfed88cf" title="Click to view the MathML source">φn to be surjective. We prove the surjectivity of φ1 for a class of trivial extensions that includes relation extensions and hence cluster-tilted algebras. Finally, we study the kernel of φ1 for any trivial extension, and give a more precise description of this kernel in the case of relation extensions.

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