For the quaternion division algebra D over a non-Archimedean local field k, and π an irreducible finite dimensional representation of D×, say with trivial central character, we prove the existence of a quadratic extension K of k such that the trivial character of K× appears in π, as well as the existence of a quadratic extension L of k such that the trivial character of L× does not appear in π....

Let Γ be a torsion free lattice in G = PGL(n+ 1,F), where n ≥ 1 and F is a non-archimedean local field. Then Γ acts on the Furstenberg boundary G/P , where P is a minimal parabolic subgroup of G. The identity element I in the crossed product C∗-algebra C(G/P ) ⋊ Γ generates a class [I] in the K0 group of C(G/P ) ⋊ Γ. It is shown that [I] is a torsion element of K0 and there is an explicit bound...

We offer an axiomatic definition of a differential algebra of gen­ eralized functions over an algebraically closed non-Archimedean field. This algebra is of Colombeau type in the sense that it contains a copy of the space of Schwartz distributions. We study the uniqueness of the objects we define and the consistency of our axioms. Next, we identify an inconsistency in the conventional Laplace t...

In this note, we use Connes’ theory of spectral triples to provide a connection between Manin’s model of the dual graph of the fiber at infinity of an Arakelov surface and the cohomology of the mapping cone of the local monodromy. Abridged English version In Arakelov theory a completion of an arithmetic surface is achieved by enlarging the group of divisors by formal linear combinations of the ...

We prove the generalized Ulam stability of ternary homomorphisms from commutative ternary semigroups into n-Banach spaces as well as into complete non-Archimedean normed spaces. Ternary algebraic structures appear in various domains of theoretical and mathematical physics, and p-adic numbers, which are the most important examples of non-Archimedean fields, have gained the interest of physicists...

Let $G$ be a connected reductive group defined over non- archimedean local field $F$. $B$ minimal $F$-parabolic subgroup with Levi factor $T$ and unipotent radical $U$. $\psi$ non-degenerate character of $U(F)$ $\lambda$ $T(F)$. $(K,\rho )$ Bushnell-Kutzko type associated to the Bernstein block $G(F)$ determined by pair $(T,\lambda )$. We study $\rho$-isotypical component $(c\text {-ind}_{U(F)}...

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.

In this paper I show that a kind of infinite-order predicate logic can be regarded as non-Archimedean or p-adic valued. I have considered two principal versions of non-Archimedean valued predicate logical calculi: p-adic valued extension of BL∀ and hyper-valued extension of à LΠ∀. These logical systems are considered for the first time. c ©2010 World Academic Press, UK. All rights reserved.

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.

‖b+ c‖ ≤ max (‖b‖, ‖c‖) then the value ‖b‖ is called non-archimedean. The thus delimited nonarchimedean values are of considerable arithmetic interest. They are useful in questions of divisibility and irreducibility and in fact often correspond exactly to the prime ideals of the given ring. This paper is devoted to the explicit construction of non-archimedean values. More specifically, given al...