Browsing by Author "Russo, Francesco"

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    On the topological entropy of nilpotent groups of finite rank
    (2024-05) Waka, Olwethu; Russo, Francesco
    The present PhD thesis deals with some finiteness conditions on the topological entropy of continuous endomorphims of periodic locally compact Heisenberg p-groups (p prime). These are relevant models of locally compact nilpotent groups and their structure may be described very well by semidirect products. Firstly, we consider the class of locally compact abelian groups that are compactly generated; we recognize a relevant subclass among these, namely the slender groups, and observe that slender groups have very small values of topological entropy for their endomorphisms. Then we investigate a more general case of nilpotent periodic locally compact p-groups, reducing the computations to maximal p-subgroups. The role of p-groups becomes somehow fundamental, so we focus on locally compact Heisenberg p-groups which are studied especially on the field Qp of p-adic rationals and on the ring Zp of p-adic integers.
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    The relevance of the Pauli group in dynamical systems with pseudo-fermions
    (2021) Bavuma, Yanga; Russo, Francesco
    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 its 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 S3 ; one orbit space comes from the free action of the quaternion group Q8 on S3 ; another orbit space comes from a similar action of the cyclic group Z(4) of order 4 on S3. 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.
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    Topics In Nonabelian Tensor Products Of Topological Groups
    (2021) Ramabulana, Mita D; Russo, Francesco
    The well-known notion of tensor product is used to describe multilinear relations between objects and enjoys many applications in pure and applied mathematics. The tensor product has been studied extensively in linear algebra with generalisations to abstract abelian group theory and modules. In this MSc thesis we study further generalisations of tensor products to non-abelian groups as well as topological groups. We encounter a rich existing theory of compact topological groups, which we are going to investigate. Finally we consider some recent problems in the theory of nonabelian tensor products of topological groups, showing a series of relevant connections between algebraic topology, topological group theory, and homological algebra