A Class of Irreducible matrix representations of an Arbitrary Inverse Semigroup
نویسندگان
چکیده
منابع مشابه
On the Irreducible Representations of a Finite Semigroup
Work of Clifford, Munn and Ponizovskĭı parameterized the irreducible representations of a finite semigroup in terms of the irreducible representations of its maximal subgroups. Explicit constructions of the irreducible representations were later obtained independently by Rhodes and Zalcstein and by Lallement and Petrich. All of these approaches make use of Rees’s theorem characterizing 0-simple...
متن کاملA construction for irreducible representations is applied to various inverse semigroup algebras
In recent years there has been a growing number of constructions of faithful irreducible representations for the semigroup algebra FS of some specific inverse semigroups S. As usual, when S has a zero element θ, the contracted semigroup algebra F0S = FS/Fθ is considered. When F = C, the interest has been on faithful irreducible ∗-representations of CS (or C0S), and also `(S) (or `0(S)), on an i...
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In this article, we characterize the involutiveness of the linear combination of the forma1A1 +a2A2 when a1, a2 are nonzero complex numbers, A1 is a quadratic or tripotent matrix,and A2 is arbitrary, under certain properties imposed on A1 and A2.
متن کاملIrreducible Matrix Representations of Finite Semigroups
Munn [9] has shown that for a semigroup S satisfying the minimal condition on principal ideals, there is a natural one-to-one correspondence between irreducible representations of S and irreducible representations vanishing at zero of its 0-simple (or simple) principal factors; for the case of S finite, see Ponizovskii [11]. On the other hand, Clifford, [3] and [4], has obtained all representat...
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ژورنال
عنوان ژورنال: Proceedings of the Glasgow Mathematical Association
سال: 1961
ISSN: 2040-6185,2051-2104
DOI: 10.1017/s2040618500034286