A rational isomorphism is a p-compact group homomorphism inducing an isomorphism on rational cohomology. Finite covering homomorphisms and nontrivial endomorphisms of simple p-compact groups are rational isomorphisms. It is shown that rational isomorphisms of p-compact groups restrict to admissible rational isomorphisms of the maximal tori and the classification of rational isomorphisms between...

Let D and A be unital and separable C∗-algebras; let D be strongly selfabsorbing. It is known that any two unital ∗-homomorphisms from D to A ⊗ D are approximately unitarily equivalent. We show that, if D is also K1-injective, they are even asymptotically unitarily equivalent. This in particular implies that any unital endomorphism of D is asymptotically inner. Moreover, the space of automorphi...

We consider elliptic operators in divergence form L = div (Φ · grad ) either on a closed Riemannian manifold or in a domain with compact closure and piecewise smooth boundary M where Φ : M → End(TM) is a positive definite symmetric smooth section of the bundle of all endomorphisms of TM . We show that the first nonzero L-eigenvalues in the closed or Dirichlet eigenvalue problems can be bounded ...

In this paper we unfold the 2-category structure of the representations of a (strict) 2-group on (a suitable version of) Kapranov and Voevodsky’s 2-category of finite dimensional 2-vector spaces and we discuss the relationship with classical representation theory of groups on finite dimensional vector spaces. In particular, we prove that the monoidal category of representations of any group G a...

Let S be a monoid of endomorphisms of a quasiprojective variety V defined over a global field K. We prove a lower bound for the size of the reduction modulo places of K of the orbit of any point α ∈ V (K) under the action of the endomorphisms from S. We also prove a similar result in the context of Drinfeld modules. Our results may be considered as dynamical variants of Artin’s primitive root c...

A presentation by generators and relations is given for the monoids of endomorphisms in the simplicial category. These monoids are submonoids of monoids one finds in Temperley-Lieb algebras, and as the monoids of Temperley-Lieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of simplicial endomorphisms axiomatized here are linked to arbitrary adjoint ...

Certain criteria are demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms of that algebra. These are then used to establish a converse to recent results of Borchers and of Wiesbrock on certain one-parameter semigroups of endomorphisms of von Neumann algebras (specifically, Type III1 factors) that appear as lightlike translations i...

Let S2 be the p-primary second Morava stabilizer group, C a supersingular elliptic curve over Fp, O the ring of endomorphisms of C, and ` a topological generator of Zp (respectively Z2 /{±1} if p = 2). We show that for p > 2 the group Γ ⊆ O[1/`]× of quasi-endomorphisms of degree a power of ` is dense in S2. For p = 2, we show that Γ is dense in an index 2 subgroup of S2. AMS classification: Pri...

A. – Let k be a field. We compute the set [ P,P ]N of naive homotopy classes of pointed k-scheme endomorphisms of the projective line P. Our result compares well with Morel’s computation in [11] of the group [ P,P ]A1 of A-homotopy classes of pointed endomorphisms of P: the set [ P,P ]N admits an a priori monoid structure such that the canonical map [ P,P ]N → [P1,P1]A1 is a group comple...

We show that among the endomorphisms of the free (non-abelian) group Fr of rank r, the set of monomorphisms (the injective endomorphisms) has density one. This contrasts with the known fact that the set of automorphisms has density zero. We show more generally that in the set of homomorphisms from one free group to another, the set of monomorphisms has density one whereas the set of epimorphism...