Connes discovered that changing the state does not change the image of the modular automorphism in the outer automorphism group of " M ".
22.
For example, for the alternating group, } }, the outer automorphism group is usually the group of order 2, with exceptions noted below.
23.
*PM : examples of outer automorphism group, id = 8682 new !-- WP guess : examples of outer automorphism group-- Status:
24.
*PM : examples of outer automorphism group, id = 8682 new !-- WP guess : examples of outer automorphism group-- Status:
25.
The alternating groups usually have an outer automorphism group of order 2, but the alternating group on 6 points has an Schur multiplier of order 6.
26.
Diagram automorphisms correspond to outer automorphisms of the Lie algebra, meaning that the outer automorphism group Out = Aut / Inn equals the group of diagram automorphisms.
27.
This exceptional outer automorphism is realized inside of the Mathieu group M 12 and similarly, M 12 acts on a set of 12 elements in 2 different ways.
28.
:Perhaps reading Inner automorphism # The inner and outer automorphism groups will give you a hint .-- Talk 15 : 52, 13 June 2007 ( UTC)
29.
We have seen above that there is a canonical homomorphism ? from the group of reals to the outer automorphism group of a von Neumann algebra, given by modular automorphisms.
30.
This corresponds to the outer automorphism that's unique to S 6 ( among symmetric groups ) .-- talk ) 14 : 15, 4 May 2010 ( UTC)
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