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

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0695247-3

Keywords:
Monoid,
algebraic,
automorphism,
-class

Article copyright:
© Copyright 1983
American Mathematical Society