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Conjugacy Classes in Algebraic Monoids II

Published online by Cambridge University Press:  20 November 2018

Mohan S. Putcha
Mohan S. Putcha*
Affiliation:
Department of Mathematics North Carolina State University Raleigh, North Carolina 27695-8205 U.S.A.
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Abstract

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Let M be a connected linear algebraic monoid with zero and a reductive unit group. We show that there exist reductive groups G1,..., Gt, each with an automorphism, such that the conjugacy classes of M are in a natural bijective correspondence with the twisted conjugacy classes of Gi, i = 1,..., t.

Keywords

20G9920M10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 3 , 01 June 1994 , pp. 648 - 661
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Carter, R. W., Finite groups of Lie type: Conjugacy classes and complex characters, Wiley, 1985.Google Scholar
2. Humphreys, J. E., Linear algebraic groups, Springer-Verlag, 1981.Google Scholar
3. Putcha, M. S., A semigroup approach to linear algebraic groups, J. Algebra 80(1983), 164–185.Google Scholar
4. Putcha, M. S., Determinant junctions on algebraic monoids, Comm. Algebra 11(1983), 695–710.Google Scholar
5. Putcha, M. S., Linear algebraic monoids, London Math. Soc. Lecture Note Series 133, Cambridge Univ. Press, 1988.Google Scholar
6. Putcha, M. S., Conjugacy classes in algebraic monoids, Trans. Amer. Math. Soc. 303(1987), 529–540.Google Scholar
7. Renner, L. E., Analogue of the Bruhat decomposition for algebraic monoids, J. Algebra 101(1986), 303–338.Google Scholar
8. Renner, L. E., Conjugacy classes of semisimple elements, and irreducible representations of algebraic monoids, Comm. Algebra 116(1988), 1933–1943.Google Scholar
9. Renner, L. E., Analogue of the Bruhat decomposition for algebraic monoids II. The length function and the trichotomy, to appear.Google Scholar