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arXiv · 1604.02758

Derivations and the first cohomology group of trivial extension algebras

Driss Bennis·Brahim Fahid
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Abstract

In this paper we investigate in details derivations on trivial extension algebras. We obtain generalizations of both known results on derivations on triangular matrix algebras and a known result on first cohomology group of trivial extension algebras. As a consequence we get the characterization of trivial extension algebras on which every derivation is inner. We show that, under some conditions, a trivial extension algebra on which every derivation is inner has necessarily a triangular matrix representation. The paper starts with detailed study (with examples) of the relation between the trivial extension algebras and the triangular matrix algebras.

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Driss Bennis, Brahim Fahid. 2017-06-06. Derivations and the first cohomology group of trivial extension algebras. https://arxiv.org/abs/1604.02758

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