相关论文: Families of unitary matrices achieving full divers…

We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.

We produce an explicit family of totally real cyclic quartic polynomials that are monogenic in many cases and, if the $abc$ conjecture holds, generate distinct monogenic quartic fields infinitely often. Additional families (also…

This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.

This paper has an expository nature. We compare the spectral properties (such as boundedness and compactness) of three families of semi-infinite matrices and point out similarities between them. The common feature of these families is that…

We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…

We describe a procedure for generating families of cyclic cubic fields with explicit fundamental units. This method generates all known families and gives new ones.

We consider Homogeneous Algebraic Riccati Equations in the general situation when the matrix of the dynamics can be "mixed". We show that in this case the equation may have infinitely many families of solutions. An analysis of these…

We demonstrate that when a graph exhibits a specific type of symmetry, it satisfies the Union Closed Conjecture(UCC). Additionally, we show that certain graph classes, such as Cylindrical Grid Graphs and Torus Grid Graphs also satisfy the…

Euclidean distance matrices corresponding to an arithmetic progression have rich spectral and structural properties. We exploit those properties to develop completely positive factorizations of translations of those matrices. We show that…

A family of algebraic surfaces with many nondegenerate real singularities is introduced with the help of a construction, which has been used in previous works for the generation of substitution tilings.

We construct a moduli space for the connected subgroups of an algebraic group and the corresponding universal family. Morphisms from an algebraic variety to this moduli space correspond to flat families of connected algebraic subgroups…

We obtain a family of new combinatorial identities for symmetric formal power series.

We present a new infinite family of full spark frames in finite dimensions arising from a unitary group representation, where the underlying group is the semi-direct product of a cyclic group by a group of automorphisms. The only previously…

We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.

In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…

Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…

We introduce a class of Banach algebras of generalized matrices and study the existence of approximate units, ideal structure, and derivations of them.

Families of objects appear in several contexts, like algebraic topology, theory of deformations, theoretical physics, etc. An unified coordinate-free algebraic framework for families of geometrical quantities is presented here, which allows…

A priori, the set of birational transformations of an algebraic variety is just a group. We survey the possible algebraic structures that we may add to it, using in particular parametrised family of birational transformations.

In this short notes, we consider multiplicities of representations in general algebraic families, especially the upper semi-continuity of homological multiplicities and the locally constancy of Euler-Poincare numbers. This generalizes the…