What are...representations?
Goal.
Explaining basic concepts of representation theory in an intuitive way.
This time.
What are...representations? Or: Matrices are cool!
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.
http://www.dtubbenhauer.com/youtube.html
Website with exercises.
http://www.dtubbenhauer.com/lecture-r...
Representation theory.
https://en.wikipedia.org/wiki/Represe...
https://en.wikipedia.org/wiki/Represe...
Representation.
https://en.wikipedia.org/wiki/Group_r...
https://mathworld.wolfram.com/GroupRe...
https://www.mathphysicsbook.com/mathe...
Faithful representation.
https://en.wikipedia.org/wiki/Faithfu...
https://ncatlab.org/nlab/show/faithfu...
https://mathworld.wolfram.com/Faithfu...
Symmetry.
https://en.wikipedia.org/wiki/Symmetr...
https://en.wikipedia.org/wiki/Categor...
Pictures used.
https://en.wikipedia.org/wiki/Rotatio...
https://www.mathphysicsbook.com/wp-co...
Pictures from https://en.wikipedia.org/wiki/Quatern...
Some books I am using (I sometimes steal some pictures from there).
https://link.springer.com/book/10.100...
https://users.metu.edu.tr/sozkap/513-...
https://link.springer.com/book/10.100...
https://math.mit.edu/~etingof/replect...
https://link.springer.com/book/10.100...
https://link.springer.com/book/10.100...
https://www.cambridge.org/core/books/...
https://link.springer.com/book/10.100...
Mathematica.
https://arxiv.org/abs/1912.10969 (Mostly for representations of Lie groups and algebras)
Magma.
https://magma.maths.usyd.edu.au/magma...
http://magma.maths.usyd.edu.au/calc/
SageMath.
https://doc.sagemath.org/html/en/cons...
https://sagecell.sagemath.org/
#representationtheory
#algebra
#mathematics