Related papers: Phase transition in the CAR algebra
We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $C^*$-algebras $B$ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on $L^2(B)$, the quantum…
Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive…
The classification of topological phases of matter is fundamental to understand and characterize the properties of quantum materials. In this paper we study phases of matter in one-dimensional open quantum systems. We define two mixed…
We define the completion of an associative algebra $A$ in a set $M=\{M_1,\dots,M_r\}$ of $r$ right $A$-modules in such a way that if $\mathfrak a\subseteq A$ is an ideal in a commutative ring $A$ the completion $A$ in the (right) module…
A notion of a quantum automorphism group of a finite quantum group, generalising that of a classical automorphism group of a finite group, is proposed and a corresponding existence result proved.
We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.
In previous work we determined automorphism groups of cyclic algebraic curves defined over fields of any odd characteristic. In this paper we determine parametric equations of families of curves for each automorphism group for such curves.
Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer…
We present an analytic proof of the existence of phase transition in the large $N$ limit of certain random noncommutaitve geometries. These geometries can be expressed as ensembles of Dirac operators. When they reduce to single matrix…
The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical…
Let $A$ be a finite group acting by automorphisms on the finite group $G$. We introduce the commuting graph $\Gamma (G,A)$ of this action and study some questions related to the structure of $G$ under certain graph theoretical conditions on…
We consider differential rings of the form (K[x; y];D), where K is an algebraically closed field of characteristic zero and D : K[x; y] \to K[x; y] is a K-derivation. We study the Automorphism Group of such a ring and give criteria for…
This is a brief introduction to the theory of Enriques surfaces over arbitrary algebraically closed fields. Some new results about automorphism groups of Enriques surfaces are also included.
Let $ k $ be a field, $ G $ a totally ordered abelian group and $ \mathbb K = k((G)) $ the maximal field of generalised power series, endowed with the canonical valuation $ v $. We study the group $ v \mathrm{-Aut} K $ of valuation…
Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…
We determine the automorphism group for some well known constructions of finite semifields. In particular, we compute the automorphism group of Sandler's semifields and in certain cases the automorphism groups of the Hughes-Kleinfeld and…
We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…
The method of direct calculation of the group of $\mathbb R$-algebra automorphisms of a Weil algebra is presented in detail. The paper is focused on the case of a one-componental group and presents two cases of values of the determinant of…
The notion of a topological phase of an insulator is based on the concept of homotopy between Hamiltonians. It therefore depends on the choice of a topological space to which the Hamiltonians belong. We advocate that this space should be…
To address the challenge of insufficient interactivity and behavioral diversity in autonomous driving decision-making, this paper proposes a Cognitive Hierarchical Agent for Reasoning and Motion Stylization (CHARMS). By leveraging Level-k…