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Results tagged with semigroups-and-monoids
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user 391
A semigroup is a set $S$ together with a binary operation that is associative. Examples of semigroups are the set of finite strings over a fixed alphabet (under concatenation) and the positive integers (under addition, maximum, or minimum). A monoid is a semigroup with a neutral element. Of course, any group is also a monoid/semigroup.
87
votes
Why aren't representations of monoids studied so much?
Whenever you see people using Young tableaux to discuss representations of $GL_n$ they include an apologetic "we'll only consider polynomial representations, i.e. not $det^{-1}$". That is to say, they …
- 27.9k
4
votes
Are orbits of an affine algebraic monoid affine?
Let $SL_2$ act on ${\mathbb A}^2$. This has two orbits, $\{\vec 0\}$ and its complement, and the latter is not affine.
- 27.9k