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On the automorphism group of a linear algebraic monoid

Author: Mohan S. Putcha
Journal: Proc. Amer. Math. Soc. 88 (1983), 224-226
MSC: Primary 20M10; Secondary 20G99
MathSciNet review: 695247
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Abstract: Let $ S$ 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 $ \mathcal{G}$-classes of $ S$, and the kernel of this homomorphism is the group of inner automorphisms of $ S$. In particular, if the $ \mathcal{G}$-classes of $ S$ are linearly ordered, then every automorphism of $ S$ is inner.

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Keywords: Monoid, algebraic, automorphism, $ \mathcal{G}$-class
Article copyright: © Copyright 1983 American Mathematical Society

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