Log24

Tuesday, May 10, 2011

Groups Acting

Filed under: General,Geometry — Tags: , — m759 @ 10:10 AM

The LA Times  on last weekend's film "Thor"—

"… the film… attempts to bridge director Kenneth Branagh's high-minded Shakespearean intentions with Marvel Entertainment's bottom-line-oriented need to crank out entertainment product."

Those averse to Nordic religion may contemplate a different approach to entertainment (such as Taymor's recent approach to Spider-Man).

A high-minded— if not Shakespearean— non-Nordic approach to groups acting—

"What was wrong? I had taken almost four semesters of algebra in college. I had read every page of Herstein, tried every exercise. Somehow, a message had been lost on me. Groups act . The elements of a group do not have to just sit there, abstract and implacable; they can do  things, they can 'produce changes.' In particular, groups arise naturally as the symmetries of a set with structure. And if a group is given abstractly, such as the fundamental group of a simplical complex or a presentation in terms of generators and relators, then it might be a good idea to find something for the group to act on, such as the universal covering space or a graph."

— Thomas W. Tucker, review of Lyndon's Groups and Geometry  in The American Mathematical Monthly , Vol. 94, No. 4 (April 1987), pp. 392-394

"Groups act "… For some examples, see

Related entertainment—

High-minded— Many Dimensions

Not so high-minded— The Cosmic Cube

One way of blending high and low—

The high-minded Charles Williams tells a story
in his novel Many Dimensions about a cosmically
significant cube inscribed with the Tetragrammaton—
the name, in Hebrew, of God.

The following figure can be interpreted as
the Hebrew letter Aleph inscribed in a 3×3 square—

The above illustration is from undated software by Ed Pegg Jr.

For mathematical background, see a 1985 note, "Visualizing GL(2,p)."

For entertainment purposes, that note can be generalized from square to cube
(as Pegg does with his "GL(3,3)" software button).

For the Nordic-averse, some background on the Hebrew connection—