相关论文: Algebraic entropy, symmetries and linearization of…

We give an exact spectral equivalence between the quantum group invariant XXZ chain with arbitrary left boundary term and the same XXZ chain with purely diagonal boundary terms. This equivalence, and a further one with a link pattern…

We study some examples when there is actually an equality in the linear algebra bound. When the vectors considered span in fact the entire space. We would like to point out that in some cases this provides some interesting extra information…

The paper develops elementary linear algebra methods to compute the determinants of the tensor symmetrizations of quadratic and hermitian forms over fields of good characteristic. Explicit results are given for the partitions $(n)$,…

We study the multiplication operation of square matrices over lattices. If the underlying lattice is distributive, then matrices form a semigroup; we investigate idempotent and nilpotent elements and the maximal subgroups of this matrix…

We give entropy estimates for two canonical non commutative shifts on $C^*$-algebras associated to some topological graphs $E=(E^0,E^1,s,r)$, defined using a basis of the corresponding Hilbert bimodule $H(E)$. We compare their entropies…

We define link and graph invariants from entropic magmas modeling them on the Kauffman bracket and Tutte polynomial. We define the homology of entropic magmas. We also consider groups that can be assigned to the families of compatible…

We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups beyond the one-dimensional (1D) setting. Our construction is…

We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of…

We study real nonsingular projective cubic fourfolds up to deformation equivalence combined with projective equivalence and prove that they are classified by the conjugacy classes of involutions induced by the complex conjugation in the…

It is shown that for non-hyperbolic real quadratic polynomials topological and quasisymmetric conjugacy classes are the same. By quasiconformal rigidity, each class has only one representative in the quadratic family, which proves that…

We present counterexamples to the lore that symmetries that cannot be gauged or made on-site are necessarily anomalous. Specifically, we construct unitary, internal symmetries of two-dimensional lattice models that cannot be consistently…

In this paper, we construct higher-order generalizations of the $A_6^{(1)}$- and $A_4^{(1)}$-surface type $q$-Painlev\'e equations from the system of partial difference equations with the consistency around a cube property by periodic…

In this article we introduce a framization of the Hecke algebra of type B. For this framization we construct a faithful tensorial representation and two linear bases. We finally construct a Markov trace on these algebras and from this trace…

In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…

We investigate the structure of two-dimensional partial cubes, i.e., of isometric subgraphs of hypercubes whose vertex set defines a set family of VC-dimension at most 2. Equivalently, those are the partial cubes which are not contractible…

We construct a diagram D, indexed by a finite partially ordered set, of finite Boolean semilattices and (v,0,1)-embeddings, with top semilattice $2^4$, such that for any variety V of algebras, if D has a lifting, with respect to the…

In this paper we describe a model of concurrency together with an algebraic structure reflecting the parallel composition. For the sake of simplicity we restrict to linear concurrent programs i.e. the ones with no loops nor branching. Such…

An algebraizable singularity is a germ of a singular holomorphic foliation which can be defined in some appropriate local chart by a differential equation with algebraic coefficients. We show that there exists at least countably many…

We consider several ways of decomposing models into parts of bounded size forming a congruence over a base, and show that admitting any such decomposition is equivalent to mutual algebraicity at the level of theories. We also show that a…

A method of classification of integrable equations on quad-graphs is discussed based on algebraic ideas. We assign a Lie ring to the equation and study the function describing the dimensions of linear spaces spanned by multiple commutators…