On representations of certain semigroups

Friedberg, Michael

doi:10.2140/pjm.1966.19.269

Pacific J. Math.

1966

DOI: 10.2140/pjm.1966.19.269

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On representations of certain semigroups

Michael Friedberg¹

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1966

1976

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Cited by 4 publications

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“…Clearly, objects admitting such representations are necessarily finite dimensional. For earlier work involving representations of (nongroup) topological semigroups, see [2] and [9]. § §2 and 3 are preparatory in nature.…”

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confidence: 99%

Linear Representations of Certain Compact Semigroups

Brown¹,

Friedberg²

1971

Transactions of the American Mathematical Society

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mentioning

confidence: 99%

Linear Representations of Certain Compact Semigroups

Brown¹,

Friedberg²

1971

Transactions of the American Mathematical Society

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Representations into the hyperspace of a compact group

Bilyeu

Lau

1976

Semigroup Forum

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A note on Haar-like measure for group-extremal semi-groups

Friedberg¹

1966

Proc. Amer. Math. Soc.

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If 5 is a compact group-extremal affine semigroup, it is natural to ask how much of the group structure of the extreme points carries over to S. In [4], the author shows it is possible to extend sufficiently many unitary representations to separate points of S; in the abelian case, this leads to sufficiently many affine semicharacters to separate points of S. We investigate in this note the possibility of extending Haar measure to S. Using results in [l], [2], and [3], it can be seen that a compact affine semigroup which supports an idempotent measure must be of the form XX Y where X and Y are compact convex sets and multiplication is given by (x, y) •(*'> y')~ix, y')-Thus, one cannot hope in general to extend Haar measure and retain all of its properties. However, we will show that if 5 is a compact group-extremal affine semigroup, then there is a probability measure p. supported on 5 (i.e. /^-measure of each nonvoid open set is positive) satisfying

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On representations of certain semigroups

Cited by 4 publications

References 3 publications

Linear Representations of Certain Compact Semigroups

Linear Representations of Certain Compact Semigroups

Representations into the hyperspace of a compact group

A note on Haar-like measure for group-extremal semi-groups

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