On a Lie algebraic approach to abelian extensions of associative algebras. (English) Zbl 1477.16015
Summary: By using a representation of a Lie algebra on the second Hochschild cohomology group, we construct an obstruction class to extensibility of derivations and a short exact sequence of Wells type for an abelian extension of an associative algebra.
MSC:
| 16E40 | (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) |
| 16W25 | Derivations, actions of Lie algebras |
| 16D20 | Bimodules in associative algebras |
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