Continuous isomorphisms onto separable groups

Isomorphisms of Groups

Definition: If (G, *) and (H, •) are groups, then a function f : G −→ H is a homomorphism if f (x * y) = f (x) • f (y) for all x, y ∈ G. Example: Let (G, *) be an arbitrary group and H = {e}, then the function f : G −→ H such that f (x) = e for any x ∈ G is a homomorphism. In fact, f (x * y) = e = e • e = f (x) • f (y).

Isomorphisms of Graph Groups

Given a graph X, define the presentation PX to have generators the vertices of X, and a relation xy = yx for each pair x, y of adjacent vertices. Let GX be the group with presentation PX, and given a field K, let KX denote the K"-algebra with presentation PX. Given graphs X and Y and a field K, it is known that the algebras KX and KY are isomorphic if and only if the graphs X and Y are isomorph...

Classical Isomorphisms for Quantum Groups

The expressions for the R̂–matrices for the quantum groups SOq2(5) and SOq(6) in terms of the R̂–matrices for Spq(2) and SLq(4) are found, and the local isomorphisms of the corresponding quantum groups are established. On leave of absence from P.N.Lebedev Physical Institute, Theoretical Department, 117924 Moscow, Leninsky prospect 53, CIS.

RATIONAL ISOMORPHISMS OF p-COMPACT GROUPS

A rational isomorphism is a p-compact group homomorphism inducing an isomorphism on rational cohomology. Finite covering homomorphisms and nontrivial endomorphisms of simple p-compact groups are rational isomorphisms. It is shown that rational isomorphisms of p-compact groups restrict to admissible rational isomorphisms of the maximal tori and the classification of rational isomorphisms between...

Automorphism groups and isomorphisms of Cayley digraphs