What are the characters of a group? | Representation theory episode 4

[@GuillermoSV]

La mejor y más clara explicación que he visto. Cuando vi un poco de teoria de grupos en la universidad quedó como un tema totalmente oscuro para mí. Ahora todo hace sentido. Excelente video!!! Me encanta esta serie

[@AllAnglesMath]

Thank you so much!

[@bartbroek9695]

amazing, if i become a patreon in some time, will the video still be available? ik zag trouwens laatst in je Q&A dat je vlaams bent, en ik had me al afgevraagd waar je accent vandaan komt, want vaak en zo ook nu kan ik een vlaams accent niet herkennen in het engels en daar had ik het toevallig die dag zelf nog met iemand over gehad. maar goed, ik kijk al je video's zodra ze uitkomen! hopelijk kan ik binnenkort eraan bijdragen :) als je nog eens een Q&A doet ben ik benieuwd wat voor muziek je luistert

[@AllAnglesMath]

The patreon-exclusive videos will be available on Patreon as long as our page exists. That's not the same thing as "forever", but you still have plenty of time 😉 Groetjes en bedankt voor je leuke commentaar!

[@강현-n1q]

I love this video!

[@AllAnglesMath]

Thank you!

[@DeathSugar]

9:08 well, that was confusing. at 1:40 you said it was homomorphism, i.e. function for mappping is character, but here you pick one one permutations and call it a character.

[@DeathSugar]

15:43 well, all those group/ring/commutativity is terms directly from number theory, so it's weird claim they aren't related.

[@TheOneMaddin]

I don't get your complaint. Group representation theory has a very different origin than number theory. There is no a priori reason to expect they are related in a not superficial way. Sure, they share some terminology. But rings, groups etc are not "owned" by number theory. There is plenty of other math out there that uses them without even thinking of numbers.

[@DeathSugar]

@@TheOneMaddin it's all started from groups and their properties - associativity, commutativity, inverse, units and the rest. NT take those properties and smash it onto different stuff - different number systems (N, Z, Q, R, C etc), matrices, graphs - basically equalizing their behaviours via homomorphisms at it's core. We came from number theory into more specific part of it. Why should it be surprising at all?

[@thomaspeck4537]

I have never seen group theory described as a branch of number theory. I don't think "number theory" means what you think it means.