Is the Diamond Lemma related to representation theory in Hopf algebras?

  • Thread starter Thread starter pivoxa15
  • Start date Start date
  • Tags Tags
    Diamond Rings
pivoxa15
Messages
2,250
Reaction score
1
Anyone know that result? Comments? How is it connected to algebra in general and what kind of algebra is it part of? It is obviously about rings but what else is it part of?
 
Physics news on Phys.org
I vaguely remember this from a course on Hopf algebras and quantum groups I followed a long time ago...
 
Count Iblis said:
I vaguely remember this from a course on Hopf algebras and quantum groups I followed a long time ago...

Aren't what you suggest related to representation theory?

So the diamond lemma of rings related to representation theory? If so in what ways?
 
pivoxa15 said:
Aren't what you suggest related to representation theory?

So the diamond lemma of rings related to representation theory? If so in what ways?

I would have to digg up my old notes. We (physics students) were following a course on Hopf algebras intended for physicists. So, the Prof. had to take into account that we don't know a lot about the ordinary algebra stuff. Somewhere in the course this "Diamond Lemma" came up...
 

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

I Meaning of "passage to the quotient"?
Replies
3
Views
453
I Trouble with a passage in Zariski & Samuel's Commutative algebra text
Replies
5
Views
638
B What unique contributions to math did linear algebra make?
Replies
19
Views
3K
A Solving algebraic equations that cannot be solved in radicals
Replies
6
Views
1K
I Splitting ring of polynomials - why is this result unfindable?
Replies
9
Views
2K
I Adjoint Representation Confusion
Replies
3
Views
3K
MHB Polynomial Rings - Lemma 1.13 from Sharp: Steps in Commutative Algebra
Replies
6
Views
2K
MHB Why is Sharp's Lemma 1.10 crucial for understanding R-algebras?
Replies
1
Views
2K
A Number Line in Synthetic differential geometry
Replies
6
Views
2K
B Hopf fibration, Bloch sphere and quantum rotations - interactive site
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top