Question

Need some help, group theory related :S Cayley table

Answer 1

nvm i think i just figured it out

Answer 2

I was doing it for physics, got like half the table done and was like wut on the second part, but then i saw this https://en.wikipedia.org/wiki/Cayley_table

Answer 3

Cayley tables are basically multiplication tables for stuff. They're pretty fun imo

Answer 4

Yeah, its pretty neat have to use an equilateral triangle and symmetries rotations and stuff yo

Answer 5

https://en.wikipedia.org/wiki/Noether%27s_theorem

Answer 6

https://www.youtube.com/watch?v=CxlHLqJ9I0A

Answer 7

Haha actually I was just doing some stuff with Lie Algebras the other day, continuous symmetries imply that there is a conserved quantity. Thx Noether

Answer 8

What's abelian group?

Answer 9

It's a group that is commutative, in other words AB=BA. Not necessarily true for a group.

Answer 10

Interesting

Answer 11

there are 4 things that a group has to have:

-it has to be "closed" (imo this is a bad word)
-it has to be associative (ab)c=a(bc)
-there's an identity element
-everything has an inverse

Answer 12

Whenever you talk about a group you have to know two things:

What's the binary operation?
What's the set of stuff?

For quantum mechanics a popular group is the binary operation of the commutator with all Hermitian operators as the set.

Another group is the operation of multiplication with the set of all the real numbers without 0,it forms an Abelian group.

Groups are probably one of my most favorite things, plus they're also strongly tied to linear algebra so matrices and groups are two great tastes that taste great together. :P