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On the automorphism group of a linear algebraic monoid

1983
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Proceedings of the American Mathematical Society
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Let 5 be a connected regular monoid with zero. It is shown that an automorphism of S is inner if and only if it sends each idempotent of S to a conjugate idempotent. In the language of semigroup theory, the automorphism group of S maps homomorphically into the automorphism group of the finite lattice of J-classes of S, and the kernel of this homomorphism is the group of inner automorphisms of S. In particular, if the Jj-classes of S are linearly ordered, then every automorphism of 5 is inner.

doi:10.1090/s0002-9939-1983-0695247-3
fatcat:esqorzpe5baddmntd2yxxdxdya