Related papers: Magnetic translation groups as group extension
In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative…
The existence of triangular and unitriangular factorizations has been extensively studied for untwisted Chevalley groups, as well as for twisted Chevalley groups of types other than ${}^2A_{2n} \ (n \geq 1)$. However, the case of twisted…
Theory of pointlike magnetic monopole with an arbitrary magnetic charge is considered. It is shown that a proper description requires making use of nonunitary representations of the rotation group and the nonassociative generalization of…
It is proved that MacLane's coherence results for monoidal and symmetric monoidal categories can be extended to some other categories with multiplication; namely, to relevant, affine and cartesian categories. All results are formulated in…
The relation between 3-cocycles arising in the Dirac monopole problem and nonassociative gauge transformations is studied. It is shown that nonassociative extension of the group U(1) allows to obtain a consistent theory of pointlike…
The irreducible representations of the group C4(direct product)V can be used to distinguish polarization eigenmodes, to account for their degeneracies and to associate them with particular magnetic crystal classes. The occurrence of this…
Translation association schemes are constructed from actions of finite groups on finite abelian groups satisfying certain natural conditions. It is also shown that the mere existence of maps from finite groups to themselves sending each…
Maxwell extension of affine algebra with additional tensorial generators is given. Using the methods of nonlinear realizations, we found the transformation rules for group parameters and corresponding generators. Gauging the Maxwell-affine…
Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms…
Group classification of a class of Benjamin-Bona-Mahony (BBM) equations with time dependent coefficients is carried out. Two equivalent lists of equations possessing Lie symmetry extensions are presented: up to point equivalence within the…
A large class of orbifold quiver gauge theories admits the action of finite Heisenberg groups of the form \prod_i Heis(Z_{q_i} x Z_{q_i}). For an Abelian orbifold generated by \Gamma, the Z_{q_i} shift generator in each Heisenberg group is…
We present a geometrically oriented classification theory for non-Abelian extensions of groupoids generalizing the classification theory for Abelian extensions of groupoids by Westman as well as the familiar classification theory for…
The aim of this work is the study of magnetic trajectories on nilmanifolds. The magnetic equation is written and the corresponding solutions are found for a family of invariant Lorentz forces on a 2-step nilpotent Lie group equipped with a…
We show that the left regular representation of Neretin groups is factorial, providing the first example of a non-discrete simple group with this property. This is based on a new criterion of factoriality for totally disconnected groups.…
Theoretical predictions underlying determinations of the fine structure constant alpha and the electron-to-proton mass ratio m_e/m_p are reviewed, with the emphasis on the bound electron magnetic anomaly g-2. The theory of the interaction…
In the paper we study inverse semigroups $\mathscr{B}(G)$, $\mathscr{B}^+(G)$, $\bar{\mathscr{B}}(G)$ and $\bar{\mathscr{B}}\,^+(G)$ which are generated by partial monotone injective translations of a positive cone of a linearly ordered…
We consider II$_1$ factors of the form $M=\bar{\bigotimes}_{G}N\rtimes G$, where either i) $N$ is a non-hyperfinite II$_1$ factor and $G$ is an ICC amenable group or ii) $N$ is a weakly rigid II$_1$ factor and $G$ is ICC group and where $G$…
We give an analog of Frobenius' theorem about the factorization of the group determinant on the group algebra of finite abelian groups and we extend it into dihedral groups and generalized quaternion groups. Furthermore, we describe the…
In this article we describe extensions of some K-theory classes of Heisenberg modules over higher-dimensional noncommutative tori to projective modules over crossed products of noncommutative tori by finite cyclic groups, aka noncommutative…
For a pair of groups $G, H$ we study pairs of actions $G$ on $H$ and $H$ on $G$ such that these pairs are compatible and non-abelian tensor products $G \otimes H$ are defined.