Inner automorphism

In abstract algebra an inner automorphism is an automorphism of a group, ring, or algebra given by the conjugation action of a fixed element, called the conjugating element. They can be realized via simple operations from within the group itself, hence the adjective "inner". These inner automorphisms form a subgroup of the automorphism group, and the quotient of the automorphism group by this subgroup is defined as the outer automorphism group.

It is related to central algebras.

Example

The Skolem–Noether theorem let us assure that each automorphism of the matrix algebra is inner (see here.

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es


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