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The characters of the symmetric inverse semigroup

Published online by Cambridge University Press:  24 October 2008

W. D. Munn
W. D. Munn
Affiliation:
The UniversityGlasgow
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Extract

There are two natural analogues of the symmetric group on n symbols in the theory of semigroups, namely, the set of all mappings of a set of n symbols into itself, and the set of all partial transformations of such a set, with the obvious definitions of multiplication. We are concerned here with the latter system. This is an inverse semigroup, and accordingly we call it the ‘symmetric inverse semigroup’. It gives rise to a semisimple algebra over a field of characteristic zero or a prime greater than n, and its matrix representations over such a field are thus completely reducible.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 1 , January 1957 , pp. 13 - 18
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

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