AG Lie-Gruppen: Yanga Bavuma (Univ. of,Capetown), Topological structure of some central products and their influence on dynamical systems

Topological structure of some central products and their influence on
dynamical systems

Vortragende: Yanga Bavuma (Univ. of,Capetown)
Einladender: Karl-Hermann Neeb

Abstract:
The group of Wolfgang Pauli is well known in mathematical physics, because it
describes some relevant symmetries in quantum dynamical systems. It is less
known its structure of finite $2$-group of order $16$, which may be decomposed
in the central product of two of ist subgroups. From this perspective, the
Pauli
group has an interesting structure at an algebraic level as well. Here a
topological perspective is added to the literature. It is described the Pauli
group as an appropriate quotient of the fundamental group of $3$-dimensional
Riemannian surfaces constructed as two distinct orbit spaces of the
$3$-dimensional sphere $\\mathbb{S}^3$; one orbit space comes from the free
action of the quaternion group $Q_8$ on $\\mathbb{S}^3$; another orbit space
comes from a similar action of the cyclic group $\\mathbb{Z}(4)$ of order $4$
on
$\\mathbb{S}^3$. Applications are illustrated for pseudo-fermionic operators,
introducing a relevant framework of quantum mechanics. This suggests a
physical
interpretation for the topological decomposition, which has been found at an
abstract level. The connection between groups of symmetries and dynamical
systems is in fact well known, but looking specifically at the algebraic and
topological decompositions of the Pauli group, we find conditions for the
existence of a Riemannian $3$-manifold whose fundamental group is
epimorphically
mapped to a central product.

Zoom link:
<https://fau.zoom.us/j/96842049915?pwd=RXE0S3VKSWlSRUI2SCtTdEhYcjUvZz09>
Meeting ID: 968 4204 9915
Passcode: 088989