In this paper we survey results related to homomorphism dualities for graphs, and more generally, for finite structures. This is related to some of the classical combinatorial problems, such as colorings of graphs and hypergraphs, and also to recently intensively studied Constraint Satisfaction Problems. On the other side dualities are related to the descriptive complexity and First Order defin...

We consider four different models of process interactions that unify and generalise models introduced and studied by Angluin et al. [AAD04] and models introduced and studied by Mazurkiewicz [Maz04a,Maz04b]. We encode these models by labelled (hyper)graphs and relabelling rules on this labelled (hyper)graphs called negotiations. Then for these models, we give complete characterisations of labell...

The law of quadratic reciprocity is a gem from number theory. In this article we show that it has a natural interpretation that can be generalized to an arbitrary finite group. Our treatment relies almost exclusively on concepts and results known at least a hundred years ago. A key role in our story is played by group characters. Recall that a character χ of a finite Abelian group G is a homomo...

‎let $m$ be a non-zero finitely generated module over a commutative noetherian local ring $(r,mathfrak{m})$ with $dim_r(m)=t$‎. ‎let $i$ be an ideal of $r$ with $grade(i,m)=c$‎. ‎in this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎the main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎tor^{r}_c(k,h^c_i(m))to kotim...

in this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a banach algebra $a$ into a semisimple banach algebra $b$ is continuous.

where α and β are nonzero complex numbers. If α, β lie in some subfield F of C, then the representations are defined over F (in fact, over Z[α±1, β±1]). The starting point for ρn(α) is the reduced Burau representation βn : Bn → GLn−1(Z[t, t −1]). For each i ≥ 1, set K(α) = {A ∈ SLn−1(C[t, t ]) : A ≡ I mod (t− α)}. The sequence {K(α)}i≥1 is a central series inK(α) = K 1(α) (i.e., Ki+j(α) ⊇ [K(α)...

In this paper we prove that every n-Jordan homomorphis varphi:mathcal {A} longrightarrowmathcal {B} from unital Banach algebras mathcal {A} into varphi -commutative Banach algebra mathcal {B} satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0, xin mathcal {A}, is an n-homomorphism. In this paper we prove that every n-Jordan homomorphism varphi:mathcal {A} longrightarrowmathcal...

This is the second paper in a series to study regular representations for vertex operator algebras. In this paper, given a module W for a vertex operator algebra V , we construct, out of the dual space W , a family of canonical (weak) V ⊗V -modules called DQ(z)(W ) parametrized by a nonzero complex number z. We prove that for V -modules W,W1 and W2, a Q(z)-intertwining map of type ( W ′ W1W2 ) ...

In this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a Banach algebra $A$ into a semisimple Banach algebra $B$ is continuous.