Related papers: Some products in fusion systems and localities
The first detailed comparison between ab initio calculations of finite fermionic superfluid systems, performed recently by Chang and Bertsch [Phys. Rev. A 76, 021603(R), (2007)] and by von Stecher, Greene and Blume [e-print…
Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A…
Fusion is defined for arbitrary lowest weight representations of $W$-algebras, without assuming rationality. Explicit algorithms are given. A category of quasirational representations is defined and shown to be stable under fusion.…
We generalize the idea of symmetry topological field theory (SymTFT) for subsystem symmetry. We propose the 2-foliated BF theory with level $N$ in $(3+1)$d as subsystem SymTFT for subsystem $\mathbb Z_N$ symmetry in $(2+1)$d. Focusing on…
We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.
We generalize the recently developped "internal" Density Functional Theory (DFT) and Kohn-Sham scheme to multicomponent systems. We obtain a general formalism, applicable for the description of multicomponent self-bound systems (as…
In this paper the concept of $\mathbb{F}$-functorial of a finite group was introduced. These functorials have many properties of the Fitting subgroup of a soluble group and the generalized Fitting subgroup of a finite group. It was shown…
Generalized topological spaces in the sense of Cs\'{a}sz\'{a}r have two main features which distinguish them from typical topologies. First, these families of subsets are not closed under intersections. Second, we allow for the possibility…
To any dg-category $T$ (over some base ring $k$), we define a $D^{-}$-stack $\mathcal{M}_{T}$ in the sense of \cite{hagII}, classifying certain $T^{op}$-dg-modules. When $T$ is saturated, $\mathcal{M}_{T}$ classifies compact objects in the…
We settle the fusion product decomposition theorem for higher-level affine Demazure modules for the cases $E^{(1)}_{6, 7, 8}, F^{(1)}_4$ and $E^{(2)}_{6}$, thus completing the main theorems of Chari et al. (J. Algebra, 2016) and Kus et al.…
We introduce the notion of a matched pair of fusion rings and fusion categories, generalizing the one for groups. Using this concept, we define the bicrossed product of fusion rings and fusion categories and we construct exact…
It is a long-standing open problem raised by Starostin to describe all finite groups with soluble centralizers of involutions. One can observe that if the centralizer fusion system of an involution is nilpotent, then the centralizer of that…
We discuss some notions of compactness and convergence relative to a specified family F of subsets of some topological space X. The two most interesting particular cases of our construction appear to be the following ones. (1) The case in…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
When locally engineering F-theory models some D7-branes for the gauge group factors are specified and matter is localized on the intersection curves of the compact parts of the world-volumes. In this note we discuss to what extent one can…
We investigate the connection between the spatiality of locale products and the earlier studies of the author on the locally fine coreflection of the products of uniform spaces. After giving a historical introduction and indicating the…
Let $E_1,\ldots,E_k$ be a collection of linear series on an algebraic variety $X$ over $\mathbb{C}$. That is, $E_i\subset H^0(X, \mathcal{L}_i)$ is a finite dimensional subspace of the space of regular sections of line bundles $…
Density functional theory (DFT) is a powerful theoretical tool widely used in such diverse fields as computational condensed matter physics, atomic physics, and quantum chemistry. DFT establishes that a system of $N$ interacting electrons…
Density Functional Theory (DFT) is one of the most used ab initio theoretical frameworks in materials science. It derives the ground state properties of a multi-atomic ensemble directly from the computation of its one-particle density \nr…
The general fluctuation theory is reviewed with special attention to the role played by different ensembles, and is extended to incorporate stationary metastable states obtained in the long time limit. The fluctuation in a quantity depends…