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

  • Context: Graduate 
  • Thread starter Thread starter pivoxa15
  • Start date Start date
  • Tags Tags
    Diamond Rings
Click For Summary

Discussion Overview

The discussion revolves around the relationship between the Diamond Lemma and representation theory in the context of Hopf algebras. Participants explore how the Diamond Lemma connects to algebra, particularly in relation to rings and its implications for representation theory.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants inquire about the connection between the Diamond Lemma and algebra, specifically questioning its relevance to rings and other algebraic structures.
  • One participant recalls a course on Hopf algebras and quantum groups, suggesting a possible link to representation theory.
  • Another participant echoes the inquiry about the relationship between the Diamond Lemma and representation theory, seeking clarification on the nature of this connection.
  • A participant notes that their understanding of the Diamond Lemma was shaped by a course designed for physics students, indicating a potential gap in foundational algebra knowledge among the audience.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the connections between the Diamond Lemma and representation theory, with no consensus reached on the specifics of these relationships.

Contextual Notes

There are indications of missing foundational knowledge among participants, particularly regarding ordinary algebra concepts, which may affect their understanding of the Diamond Lemma's implications.

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...
 

Similar threads

Undergrad Meaning of "passage to the quotient"?
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Near-Rings with Noncommutative Addition and Two-Sided Distributivity
  • · Replies 4 ·
Replies
4
Views
3K
Graduate What are Modular Lie Algebras and How Do They Apply to Function Spaces?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Solving algebraic equations that cannot be solved in radicals
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Trouble with a passage in Zariski & Samuel's Commutative algebra text
  • · Replies 5 ·
Replies
5
Views
2K
High School What unique contributions to math did linear algebra make?
  • · Replies 19 ·
Replies
19
Views
4K
MHB Polynomial Rings - Lemma 1.13 from Sharp: Steps in Commutative Algebra
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Adjoint Representation Confusion
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Splitting ring of polynomials - why is this result unfindable?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Differences between left vs right actions in some group theory questions
  • · Replies 1 ·
Replies
1
Views
1K