Related papers: Metamorphism as a covariant transform for the SSR …
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of…
Symmetric $k$-varieties generalize Riemannian sym\-me\-tric spaces to reductive groups defined over arbitrary fields. For most perfect fields, it is known that symmetric $k$-varieties are in one-to-one correspondence with isomorphy classes…
The notion of mixed representations of quivers can be derived from ordinary quiver representations by considering the dual action of groups on "vertex" vector spaces together with the usual action. A generating system for the algebra of…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner…
Metasurfaces -- ultrathin structures composed of subwavelength optical elements -- have revolutionized light manipulation by enabling precise control over electromagnetic waves' amplitude, phase, polarization, and spectral properties.…
Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…
The change of variable theorem is proved under the sole hypothesis of differentiability of the transformation. Specifically, it is shown under this hypothesis that the transformed integral equals the given one over every measurable subset…
One considers certain degenerations of the generic symmetric matrix over a field $k$ of characteristic zero and the main structures related to the determinant $f$ of the matrix, such as the ideal generated by its partial derivatives, the…
For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…
The paper is concerned with `geometrization' of smooth (i.e. with open stabilizers) representations of the automorphism group of universal domains, and with the properties of `geometric' representations of such groups. As an application, we…
We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants…
We study finite-dimensional representations of the Kauffman skein algebra of a surface S. In particular, we construct invariants of such irreducible representations when the underlying parameter q is a root of unity. The main one of these…
We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm…
Given a differential equation with infinite-dimensional symmetry pseudo-group it is shown, using an example, that it is generally not possible to construct enough joint invariants to form an invariant numerical scheme of the equation. To…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
We investigate a conformal-like transformation for which the spacetime interval is invariant.
We give a survey of some recent results on the fusion semirings of compact quantum groups (computations of and applications to discrete quantum groups) by using the following simplifying terminology: we say that a compact quantum group G is…
A transfer is a group homomorphism from a finite group to an abelian quotient group of a subgroup of the group. In this paper, we explain some of the properties of transfers by using noncommutative determinants. These properties enable us…
We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…