Zobrazeno 1 - 10
of 221
pro vyhledávání: '"RUSSO, FRANCESCO G."'
Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study unitary repr
Externí odkaz:
http://arxiv.org/abs/2402.13619
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 $P_2$ o
Externí odkaz:
http://arxiv.org/abs/2308.05185
The notion of conditional coproduct of a family of abelian pro-Lie groups in the category of abelian pro-Lie groups is introduced. It is shown that the cartesian product of an arbitrary family of abelian pro-Lie groups can be characterized by the uni
Externí odkaz:
http://arxiv.org/abs/2304.11544
The factorization number $F_2(G)$ of a finite group $G$ is the number of all possible factorizations of $G=HK$ as product of its subgroups $H$ and $K$, while the subgroup commutativity degree $\mathrm{sd}(G)$ of $G$ is the probability of finding two
Externí odkaz:
http://arxiv.org/abs/2304.08170
Autor:
Russo, Francesco G., Waka, Olwethu
We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting behaviour
Externí odkaz:
http://arxiv.org/abs/2304.08156
Publikováno v:
In Journal of Algebra 1 December 2024 659:148-182
Publikováno v:
Math. Ann. 388, 615-674 (2024)
Let $\alpha : {\mathbb R} \to Aut(G)$ define a continuous ${\mathbb R}$-action on the topological group $G$. A unitary representation $\pi^\flat$ of the extended group $G^\flat := G \rtimes_\alpha {\mathbb R}$ is called a ground state representation
Externí odkaz:
http://arxiv.org/abs/2108.00757
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
Externí odkaz:
http://arxiv.org/abs/2104.02354
Autor:
Bagarello, Fabio, Russo, Francesco G.
The present paper is the third contribution of a series of works, where we investigate pseudo--bosonic operators and their connections with finite dimensional Lie algebras. We show that all finite dimensional nilpotent Lie algebras (over the complex
Externí odkaz:
http://arxiv.org/abs/2002.09727
Autor:
Rocchetto, Andrea, Russo, Francesco G.
For any $m \ge 1$ and odd prime power $\mathtt{q}=\mathtt{p}^m$, for $\mathtt{q}=2$, and for any $n \ge 1$, we show a result of decomposition for Pauli groups $\mathcal{P}_{n,\mathtt{q}}$ in terms of weak central products. This can be used to describ
Externí odkaz:
http://arxiv.org/abs/1911.10158