Related papers: On Realization and Isomorphism Problems for Formal…
We show that all isomorphism classes of even rank Tambara-Yamagami categories arise as $\mathbb{Z}_2$-twisted representations of conformal nets. As a consequence, we show that their Drinfel'd centers are realized by (generalized) orbifolds…
Thimble regularization as a solution to the sign problem has been successfully put at work for a few toy models. Given the non trivial nature of the method (also from the algorithmic point of view) it is compelling to provide evidence that…
Associating to each pre-order on the indices 1,...,n the corresponding structural matrix ring, or incidence algebra, embeds the lattice of n-element pre-orders into the lattice of n x n matrix rings. Rings within the order-convex hull of…
In this article, we explore the problem of determining isomorphisms between the twisted complex group algebras of finite $p$-groups. This problem bears similarity to the classical group algebra isomorphism problem and has been recently…
This paper studies modular forms of rank four and level one. There are two possiblities for the isomorphism type of the space of modular forms that can arise from an irreducible representation of the modular group of rank four, and we…
We investigate linearity of amalgams of subgroups of algebraic groups along intersections with algebraic subgroups. In the process, we establish linearity of certain "doubles" of linear groups, and obtain new examples of finitely generated…
Our main purpose is to give multiple examples for using the available implementations for computing the normalization of an affine ring, computing the minimial generators of the normalization as an algebra over the original ring and…
In this paper, we are mainly interested in the two questions "which are the commutative rings on which every finitely presented modules is [Formula: see text]-periodic (respectively, [Formula: see text]-periodic)?". It is proved that these…
Numerical computations involving rational matrices often benefit from preserving underlying matrix structures such as symmetry, Hermitian properties, or sparsity that reflect physical, geometric, or algebraic characteristics of the system.…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
The problem of diagonalizing a class of complicated matrices, to be called ultrametric matrices, is investigated. These matrices appear at various stages in the description of disordered systems with many equilibrium phases by the technique…
We study pairs of finitely generated modules over a principal ideal domain and their corresponding matrix representations. We introduce equivalence relations for such pairs and determine invariants and canonical forms.
We introduce a systematic method to solve a type of Cartan's realization problem. Our method builds upon a new theory of Lie algebroids and Lie groupoids with structure group and connection. This approach allows to find local as well as…
We present foundational work on standard bases over rings and on Boolean Groebner bases in the framework of Boolean functions. The research was motivated by our collaboration with electrical engineers and computer scientists on problems…
We say that a digraph is essentially cyclic if its Laplacian spectrum is not completely real. The essential cyclicity implies the presence of directed cycles, but not vice versa. The problem of characterizing essential cyclicity in terms of…
We investigate the transfer of regularity between commutative, noetherian, local rings through a class of local homomorphisms which we call basically regular. We give numerical characterizations of these maps, investigate their behavior…
Given a fibration over the circle, we relate the eigenspace decomposition of the algebraic monodromy, the homological finiteness properties of the fiber, and the formality properties of the total space. In the process, we prove a more…
In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of…
We prove that if two finite metacyclic groups have isomorphic rational group algebras, then they are isomorphic. This contributes to understand where is the line separating positive and negative solutions to the Isomorphism Problem for…
The author constructs the moduli of representations whose images generate the subalgebra of upper triangular matrices (up to inner automorphisms) of the full matrix ring for any groups and any monoids.