Ciro Santilli @cirosantilli  40

In the classification of finite simple groups, groups of Lie type are a set of infinite families of simple lie groups. These are the other infinite families besides te cyclic groups and alternating groups.

A decent list at: en.wikipedia.org/wiki/List_of_finite_simple_groups, en.wikipedia.org/wiki/Group_of_Lie_type is just too unclear. The groups of Lie type can be subdivided into:

The first in this family discovered were a subset of the Chevalley groups $A_n(q)$ by Galois: $PSL(2,p)$, so it might be a good first one to try and understand what it looks like.

TODO understand intuitively why they are called of Lie type. Their names $A_n$, $B_n$ seem to correspond to the members of the classification of simple Lie groups which are also named like that.

But they are of course related to Lie groups, and as suggested at Video "Yang-Mills 1 by David Metzler (2011)" part 2, the continuity actually simplifies things.

Uniqueness results for the composition series of a group.

sphere with two Möbius strips stuck into it as per the classification of closed surfaces.

The idea tha taking the limit of the non-classical theories for certain parameters (relativity and quantum mechanics) should lead to the classical theory.

It appears that classical limit is only very strict for relativity. For quantum mechanics it is much more hand-wavy thing. See also: Subtle is the Lord by Abraham Pais (1982) page 55.

Intuition, please? Example? mathoverflow.net/questions/278641/intuition-for-symplectic-groups The key motivation seems to be related to Hamiltonian mechanics. The two arguments of the bilinear form correspond to each set of variables in Hamiltonian mechanics: the generalized positions and generalized momentums, which appear in the same number each.

Seems to be set of matrices that preserve a skew-symmetric bilinear form, which is comparable to the orthogonal group, which preserves a symmetric bilinear form. More precisely, the orthogonal group has:and its generalization the indefinite orthogonal group has:where S is symmetric. So for the symplectic group we have matrices Y such as:where A is antisymmetric. This is explained at: www.ucl.ac.uk/~ucahad0/7302_handout_13.pdf They also explain there that unlike as in the analogous orthogonal group, that definition ends up excluding determinant -1 automatically.

Therefore, just like the special orthogonal group, the symplectic group is also a subgroup of the special linear group.

All non-clade groups are evil. All non-clade terms must be forgotten. Some notable ones:

It is those early splinter groups that make it so clear that religion is fake. We believed in Judaism. Now we believe in Jesus. Oh, but wait, actually Judaism is now semi fake, and we don't live by Jewish law anymore.

That self blame, imminent end of the world and hatred for tax collectors stuff is a bit over the top, you should chill man.

But please keep the parables coming.

Ciro Santilli had to see this in a few separate places, until he underestood: that little pictur emust be a thing! Examples: