arXiv subjects

Yanga Bavuma

Publications and source records attributed to Yanga Bavuma.

4 recordsLinked to original sources

arXiv2026

Some Consequences of the Grunewald-O'Halloran Conjecture for Pseudoquonic Operators

Investigating a recent positive solution of a conjecture of Grunewald and O'Halloran for complex finite dimensional nilpotent Lie algebras, we are in the position to find results of existence and uniqueness for the construction of complex nilpotent Lie algebras of arbitrary dimension via pseudobosonic operators. We involve the so-called theory of the deformation of Lie algebras of Gerstenhaber, in order to prove our main results. There isn't a generalized version of the Grunewald-O'Halloran Conjecture when we consider pseudoquonic operators, which specialize to pseudobosonic operators in many cirumstances. Therefore we prove a result of existence (and a direct construction) of pseudobosonic $O^*$-algebras of operators, but leave open the problem of the uniqueness of the construction.

math-ph↗

arXiv2025

On the subdirect product of graph bundles

The subdirect product of two finite groups $A$ and $B$ is defined as a subgroup of the direct product $A \times B$, which is a well-known notion in finite group theory. While it is clear that, under appropriate choices of sets of generators $S$, $S_A$ and $S_B$, the Cayley graph $Cay(A \times B, S)$ corresponds to the Cartesian product $Cay(A, S_A) \square Cay(B, S_B)$ of two graphs, there is no analogue at the level of graph product that reflects the notion of subdirect product of groups. This is precisely the problem which we discuss here. By using the concept of graph bundles and the corresponding pullbacks, we introduce an operation on graph bundles such that the Cayley graph of the subdirect product of two groups can be described as the total space of the product of the Cayley graphs. This allows us to define the so-called ``network $K$-theory group of a graph'', inspired by the notion of topological $K$-theory, and we are able to investigate an interesting functor from the category of graphs to the category of abelian groups.

math.CO↗

arXiv2023

On the Pauli group on 2-qubits in dynamical systems with pseudofermions

The group of matrices $P_1$ of Pauli is a finite 2-group of order 16 and plays a fundamental role in quantum information theory, since it is related to the quantum information on the 1-qubit. Here we show that both $P_1$ and the Pauli 2-group $P_2$ of order 64 on 2-qubits, other than in quantum computing, can also appear in dynamical systems which are described by non self-adjoint Hamiltonians. This will allow us to represent $P_1$ and $P_2$ in terms of pseudofermionic operators.

math-ph↗

arXiv2021

Topological decompositions of the Pauli group and their influence on dynamical systems

In the present paper we show that it is possible to obtain the well known Pauli group $P=\langle X,Y,Z \ | \ X^2=Y^2=Z^2=1, (YZ)^4=(ZX)^4=(XY)^4=1 \rangle $ of order $16$ as an appropriate quotient group of two distinct spaces of orbits of the three dimensional sphere $S^3$. The first of these spaces of orbits is realized via an action of the quaternion group $Q_8$ on $S^3$; the second one via an action of the cyclic group of order four $\mathbb{Z}(4)$ on $S^3$. We deduce a result of decomposition of $P$ of topological nature and then we find, in connection with the theory of pseudo-fermions, a possible physical interpretation of this decomposition.

math-ph↗