Abstract
It is shown that properties of the structure of a finite semigroup S such as the order of the set ofJ of S and the existence of normal subsemigroups may be deduced from the knowledge of the characters of the irreducible representations of S. The character table of the full transformation semigroup T4 of a four-element set is given.
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References
Clifford, A.H. and G.B. Preston,The algebraic theory of semigroups I,II, Providence 1961, 1967
Curtis, C.W. and I. Reiner,Representation theory of finite groups and associative algebras, New York 1962
Grassmann, H.,Conjugation in semigroups and finite dimensional algebras, to appear in Beiträge Alg. Geom.
Ljapin, E.S.,Polugruppy, Moscou 1960
McAlister, D.B.,Representations of semigoups by linear transformations I, II, Semigroup Forum 2 (1971) 189–236, 282–320
McAlister, D.B.,Characters of finite semigroups, J. Alg. 22 (1972), 183–200
Munn, W.D.,The characters of the symmetric inverse semigroup, Proc. Cambridge Phil. Soc. 53 (1957), 13–18
Serre, J.P.,Representations lineaires des groupes finis, Paris 1967
James, G.D.,The representation theory of the symmetric group, Lecture notes in mathematics 682, Berlin, Heidelberg, New York 1978
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Communicated by H.-J. Hoehnke
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Grassmann, H. Characters and the structure of finite semigroups. Semigroup Forum 30, 211–220 (1984). https://doi.org/10.1007/BF02573450
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DOI: https://doi.org/10.1007/BF02573450