MHB Finding a Cayley Table for a Groupoid: an Example

  • Thread starter Thread starter mathmari
  • Start date Start date
  • Tags Tags
    Example Table
Click For Summary
To find the Cayley table for the groupoid $(2^{\{a,b\}},\setminus )\times (\{0,1\},\min )$, one must understand the operations involved. The Cayley table is constructed by determining the results of the operations at the intersections of rows and columns corresponding to elements of the groupoid. However, challenges arise due to the nature of the operations and the specific properties of the elements involved, which may complicate direct application of the definitions. Clarification on the definitions and the operations is necessary to accurately fill out the table. Understanding these nuances is essential for successfully constructing the Cayley table.
mathmari
Gold Member
MHB
Messages
4,984
Reaction score
7
Hey! :o

Could you give me a hint how we can find the Cayley table of a groupoid?

For example for the groupoid $(2^{\{a,b\}},\setminus )\times (\{0,1\},\min )$. (Wondering) ( $\setminus$ means the set difference )
 
Physics news on Phys.org
mathmari said:
For example for the groupoid $(2^{\{a,b\}},\setminus )\times (\{0,1\},\min )$.
Why can't you write it by definition?
 
Evgeny.Makarov said:
Why can't you write it by definition?

What do you mean? (Wondering)
 
You have the definition of Cayley table: at the intersection of row $x$ and column $y$ you write the result of the operation on $x$ and $y$. You also have the definition of the operation. What prevents you from filling the table?
 

Thread 'Confusion about the Moyal-Weyl twist'

I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...
View full post »

Similar threads

MHB Groups as Groupoids with One Object
  • · Replies 2 ·
Replies
2
Views
3K
MHB Describes elements of D_5 using SAGE
  • · Replies 6 ·
Replies
6
Views
2K
MHB The axioms of a vector space are satisfied
  • · Replies 10 ·
Replies
10
Views
2K
MHB Is Every Non-Zero Element in a Finite Ring Invertible?
  • · Replies 23 ·
Replies
23
Views
4K
Automorphism of these Cayley graphs
  • · Replies 1 ·
Replies
1
Views
2K
MHB Does \(B\) Span Algebraically \(E\) Over \(F\)?
  • · Replies 1 ·
Replies
1
Views
2K
MHB T31 vector subtraction is not commutative and not associative.
  • · Replies 5 ·
Replies
5
Views
2K
MHB Method of least square: initial position & velocity
  • · Replies 9 ·
Replies
9
Views
2K
MHB Which of the group axioms are satisfied?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Tough lemma on locally finite refinement
  • · Replies 8 ·
Replies
8
Views
2K