Table legend:S: Is this algebra simple? (Yes or No)SS: Is this algebra semi-simple? (Yes or No)Lie algebra Description S SS Remarks dim/RR the real numbers, the Lie bracket is zero 1Rn the Lie brac ...
Column legendCM: Is this group G compact? (Yes or No)\pi_0: Gives the group of components of G. The order of the component group gives the number of connected components. The group is connected if and ...
This article gives a table of some common Lie groups and their associated Lie algebras.The following are noted: the topological properties of the group (dimension; connectedness; compactness; the natu ...
Zn: the cyclic group of order n (the notation Cn is also used; it is isomorphic to the additive group of Z/nZ).Dihn: the dihedral group of order 2n (often the notation Dn or D2n is used )Sn: the symme ...
The list can be used to determine which known group a given finite group G is isomorphic to: first determine the order of G, then look up the candidates for that order in the list below. If you know w ...
Simple Lie groupsUnfortunately, there is no generally accepted definition of a simple Lie group. In particular, it is not necessarily defined as a Lie group that is simple as an abstract group. Author ...
An apeirotope is, like any other polytope, an unbounded hyper-surface. The difference is that whereas a polytope's hyper-surface curls back on itself to close round a finite volume of hyperspace, an a ...
The two-dimensional polytopes are called polygons. Regular polygons are equilateral and cyclic. A p-gonal regular polygon is represented by Schl?fli symbol {p}.Usually only convex polygons are consid ...
This table shows a summary of regular polytope counts by dimension.Dimension Convex Nonconvex ConvexEuclideantessellations Convexhyperbolictessellations Nonconvexhyperbolictessellations Hyperbolic Tes ...
This page lists the regular polytopes in Euclidean, spherical and hyperbolic spaces. The Schl?fli symbol notation describes every regular polytope, and is used widely below as a compact reference nam ...
