Related papers: Discrete Anomalies of Binary Groups
Within supersymmetric SU(5) Grand Unified Theory, we present several new scenarios with anomaly free flavor symmetry U(1)_F. Within each scenario, a variety of cases offer many possibilities for phenomenologically interesting model…
We define the notion of duality categories as generalization of duality groups. Two examples are treated. The first is the Serre duality in the categories of strict polynomial functors. The second concerns finite complexes. We show in…
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…
In this paper we use families of finite subgroups to study Grothendieck rings associated to certain discrete groups, such as the arithmetic ones.
A brief review of bicovariant differential calculi on finite groups is given, with some new developments on diffeomorphisms and integration. We illustrate the general theory with the example of the nonabelian finite group S_3.
We study natural conditions on essentially discrete spectral triples by which the quantum differential $da$ belongs to the ideal generated by the unit length $ds=D^{-1}$. We also study upper and lower bounds on the singular values of the…
The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry…
We consider the su(2) and su(3) affine theories on a cylinder, from the point of view of their discrete internal symmetries. To this end, we adapt the usual treatment of boundary conditions leading to the Cardy equation to take the symmetry…
Extending the investigations about the theory of duals, we analyze duals built up with the aid of discrete symmetry operators. We scrutinize algebraic and physical constraints (encompassing them in a theoretical scope) in order to verify…
In this paper a loophole in the SU(2) gauge anomaly is presented. It is shown that using several topological tools a theory can be designed that implements the quantization of a single Weyl doublet anomaly free while keeping the non-abelian…
We study locally definable abelian groups $\CU$ in various settings and examine conditions under which the quotient of $\CU$ by a discrete subgroup might be definable. This turns out to be related to the existence of the type-definable…
We comment on aspects of discrete anomaly conditions focussing particularly on $R$ symmetries. We review the Green-Schwarz cancellation of discrete anomalies, providing a heuristic explanation why, in the heterotic string, only the…
In this paper, we determine the dimension of the Terwilliger algebras of non-abelian finite groups admitting an abelian subgroup of index 2 by showing that they are triply transitive. Moreover, we give a complete characterization of the…
We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.
The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the properties of dual dimonoids. In the class of noncommutative…
We propose an axiomatic approach towards studying unlikely intersections by introducing the framework of distinguished categories. This includes commutative algebraic groups and mixed Shimura varieties. It allows us to define all basic…
We study anomalies of discrete internal global symmetry $G$ in two-dimensional rational conformal field theories based on twisted torus partition functions. The anomaly of $G$ can be seen from the noncommutativity of two symmetry lines…
We have investigated the modular binary octahedral group $2O$ as a flavor symmetry to explain the structure of Standard Model. The vector-valued modular forms in all irreducible representations of this group are constructed. We have…
We provide a complete classification of the singularities of cluster algebras of finite cluster type. This extends our previous work about the case of trivial coefficients. Additionally, we classify the singularities of cluster algebras for…
This paper studies weakly mixing (singular) and mixing masas in type $\rm{II}_{1}$ factors from a bimodule point of view. Several necessary and sufficient conditions to characterize the normalizing algebra of a masa are presented. We also…