What is...representation theory of monoids?

Goal.
Explaining basic concepts of representation theory in an intuitive way.

This time.
What is...representation theory of monoids? Or: What to expect.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Disclaimer.
Representation theory is a vast field, and a representation could be of a group, an associative algebra, a Lie algebra etc., and these even in flavors. These subfields are similar, but then also different in nature. So to be precise, this video series is mostly about finite dimensional representations of finite groups and monoids.

Slides.

Website with exercises.

Representation theory.

Representation.

Monoids.

The theory of monoids.

Some easy GAP code
LoadPackage("semigroups");
S := FullTransformationMonoid(3);

Dot string can easily be converted to e.g. png
One can change the monoid – there are a lot of predefined ones in GAP; alternatively input via e.g. generators & relations

Pictures used.
Picture created using the GAP code above

Some books I am using (I sometimes steal some pictures from there).

Mathematica.

Magma.

SageMath.

GAP.

#representationtheory
#algebra
#mathematics

[RepTheoAndFriends]

Finally, the most anticipated representation theory video ever!