We consider an extension of Lafont’s Interaction Nets, called Multiport Interaction Nets, and show that they are a model of concurrent computation by encoding the full π-calculus in them. We thus obtain a faithful graphical representation of the π-calculus in which every reduction step is decomposed in fully local graph-rewriting rules.

We prove an explicit formula for the invariant μ(g) for finite-dimensional semisimple, and reductive Lie algebras g over C. Here μ(g) is the minimal dimension of a faithful linear representation of g. The result can be used to study Dynkin’s classification of maximal reductive subalgebras of semisimple Lie algebras.

We prove that a dense subgroup of Homeo+(I) is not elementary amenable and (if it is finitely generated) has infinite girth. We also show that the topological group Homeo+(I) does not satisfy the Stability of the Generators Property, moreover, any finitely subgroup of Homeo+(I) admits a faithful discrete representation in it.

Given a representation of compact Lie group and state we define probability measure on the coadjoint orbits dominant weights by considering decomposition into irreducible components. For large tensor powers independent copies show that induced distributions converge to value moment map. faithful states prove measures satisfy deviation principle with an explicitly given rate function.

Multiply sectioned Bayesian networks (MSBNs) were originally proposed as a modular representation of uncertain knowledge by sectioning a large Bayesian network (BN) into smaller units. More recently, hierarchical Markov networks (HMNs) were developed in part as an hierarchical representation of the flat BN. In this paper, we compare the MSBN and HMN representations. The MSBN representation does...

For each nontrivial semisimple Hopf algebra H of dimension sixteen over $\mathbb {C}$ , the smallest inner-faithful representation acting on a quadratic AS regular A 2 or 3, homogeneously and preserving grading, is determined. Each invariant subring AH When also regular, thus providing generalization Chevalley–Shephard–Todd Theorem, we say that reflection for A.

Given a finitely generated group Γ, directed graph Λ, and map R:Λ→Γ, we introduce the notion of an (R,Λ)-directed Anosov representation. This is weakening representations. Our main theorem gives procedure to construct representations using Fock-Goncharov positivity. As application our theorem, large families primitive stable from F2 PGL(V), including non-discrete non-faithful examples.

In the present paper, we study certain quotients of étale fundamental group a hyperbolic curve over field. We prove that action outer automorphism quotient an algebraically closed field on its conjugacy classes open subgroups is faithful. Also, that, if k either number or p-adic local field, then Galois representation associated to geometric ℙk1\{0,1,∞} injective.

With every (strict or normal) unital endomorphism of the algebra of all adjointable operators on a Hilbert module there is associated a correspondence (that is, a Hilbert bimodule) such that the endomorphism can be recovered as amplification of the identity representation with that correspondence. In these notes we show the converse of this statement in the case of strongly full W–correspondenc...