34
votes
4answers
840 views

Algebra: Best mental images

I'm curious how people think of Algebras (in the universal sense, i.e., monoids, groups, rings, etc.). Cayley diagrams of groups with few generators are useful for thinking about group actions on ...
6
votes
2answers
103 views

An example of a Lie group

I have a trouble learning Lie groups --- I have no canonical example to imagine while thinking of a Lie group. When I imagine a manifold it is usually some kind of a 2D blanket or a circle/curve or a ...
6
votes
5answers
198 views

Cayley table group visualization

how can I make graphics like this? random colors. I got a script in GAP that prints rows of numbers but I want it colored just random colors ...
5
votes
3answers
341 views

Visualizing quotient groups: $\mathbb{R/Q}$

I was wondering about this. I know it is possible to visualize the quotient group $\mathbb{R}/\mathbb{Z}$ as a circle, and if you consider these as "topological groups", then this group (not ...
5
votes
2answers
168 views

linearly arranging the group tables of groups of order 128

I'm planning to make a video that shows color coded group tables for all 2328 groups of order 128 -- at 128$\times$128 pixels at 24 frames a second I think I get 97 seconds of video. Is there some ...