Related papers: Computing isomorphisms between lattices

Let $G$ be a reductive algebraic group over a $p$-adic field or number field $K$, and let $V$ be a $K$-linear faithful representation of $G$. A lattice $\Lambda$ in the vector space $V$ defines a model $\hat{G}_{\Lambda}$ of $G$ over…

We show that every word hyperbolic, surface-by-(noncyclic) free group Gamma is as rigid as possible: the quasi-isometry group of Gamma equals the abstract commensurator group Comm(Gamma), which in turn contains Gamma as a finite index…

We classify surjective lattice homomorphisms $W\to W'$ between the weak orders on finite Coxeter groups. Equivalently, we classify lattice congruences $\Theta$ on $W$ such that the quotient $W/\Theta$ is isomorphic to $W'$. Surprisingly,…

Let $Q$ be a finite quiver of Dynkin type and $\Lambda=\Lambda_Q$ be the preprojective algebra of $Q$ over an algebraically closed field $k$. Let $\mathcal {T}_\Lambda$ be the mutation graph of maximal rigid $\Lambda$ modules. Geiss,…

We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible…

Fixed an algebraic scheme $Y$. We suggest a definition for the conjugate of an algebraic scheme $X$ over $Y$ in an evident manner; then $X$ is said to be Galois closed over $Y$ if $X$ has a unique conjugate over $Y$. Now let $X$ and $Y$…

We show that one can formulate an algebra with lattice ordering so as to contain one quantum and five classical operations as opposed to the standard formulation of the Hilbert space subspace algebra. The standard orthomodular lattice is…

We present norm criteria for the existence of anti-automorphisms, as well as explicit constructions of anti-automorphisms, both on cyclic and generalized cyclic algebras. Our approach describes anti-automorphisms as polynomial maps and…

We introduce a category of dual pairs of finite locally free algebras over a ring. This gives an efficient way to represent finite locally free commutative group schemes. We give a number of algorithms to compute with dual pairs of…

We prove that the classification problem for graphs and several types of algebraic lattices (distributive, congruence and modular) up to isomorphism contains the classification problem for pairs of matrices up to simultaneous similarity.

Let G be a real semisimple Lie group with no compact factors and finite centre, and let $\Lambda$ be a lattice in G. Suppose that there exists a homomorphism from $\Lambda$ to the outer automorphism group of a right-angled Artin group…

This is a study of algebras with involution that become isomorphic over a separable closure of the base field to a tensor product of two composition algebras. We classify these algebras, provide criteria for isomorphism and isotopy, and…

We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…

We develop a Galois theory for systems of linear difference equations with an action of an endomorphism {\sigma}. This provides a technique to test whether solutions of such systems satisfy {\sigma}-polynomial equations and, if yes, then…

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…

We explore whether a root lattice may be similar to the lattice $\mathscr O$ of integers of a number field $K$ endowed with the inner product $(x, y):={\rm Trace}_{K/\mathbb Q}(x\cdot\theta(y))$, where $\theta$ is an involution of $K$. We…

Let Lambda be a tiled R-order. We give a description of Aut_R(Lambda) as the semidirect product of Inn(Lambda) and a certain subgroup of Aut(Q(Lambda)), where Q(Lambda) is the link graph of Lambda. Additionally, we give criteria for…

We introduce a class of countable groups by some abstract group-theoretic conditions. It includes linear groups with finite amenable radical and finitely generated residually finite groups with some non-vanishing $\ell^2$-Betti numbers that…

In this paper, we continue with the results in \cite{Pg} and compute the group of quasi-isometries for a subclass of split solvable unimodular Lie groups. Consequently, we show that any finitely generated group quasi-isometric to a member…

The theme of the first two sections, is to prepare the framework of how from a "complicated" family of index models I in K_1 we build many and/or complicated structures in a class K_2. The index models are characteristically linear orders,…