We prove that any affine algebraic monoid can be obtained as the endomorphisms’ monoid of a finite-dimensional (nonassociative) algebra.

We study C*-algebra endomorphims which are special in a weaker sense w.r.t. the notion introduced by Doplicher and Roberts. We assign to such endomorphisms a geometrical invariant, representing a cohomological obstruction for them to be special in the usual sense. Moreover, we construct the crossed product of a C*-algebra by the action of the dual of a (nonabelian, noncompact) group of vector b...

In this paper we propose a general recipe for calculating the automorphism groups of semigroups consisting of partial endomorphisms of relational structures with a single m-ary relation for any m ∈ N over a finite set. We use this recipe to determine the automorphism groups of the following semigroups: the full transformation semigroup, the partial transformation semigroup, and the symmetric in...

The purpose of these notes is to provide an introduction to the Steenrod algebra in an algebraic manner avoiding any use of cohomology operations. The Steenrod algebra is presented as a subalgebra of the algebra of endomorphisms of a functor. The functor in question assigns to a vector space over a Galois field the algebra of polynomial functions on that vector space: the subalgebra of the endo...

Introducing the notions of (inner) σ-derivation, (inner) σ-endomorphism and oneparameter group of σ-endomorphisms (σ-dynamics) on a Banach algebra, we correspond to each σ-dynamics a σ-derivation named as its σ-infinitesimal generator. We show that the σ-infinitesimal generator of a σ-dynamics of inner σ-endomorphisms is an inner σ-derivation and deal with the converse. We also establish a nice...

This paper introduces the truncator map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify its periodic orbits using properties of endomorphisms of the resulting algebraic structure. A stochastic model is constructed on these endomorphisms, which leads to th...

We generalize the construction of canonical algebraic curvature tensors by selfadjoint endomorphisms of a vector space to arbitrary endomorphisms. Provided certain basic rank requirements are met, we establish a converse of the classical fact that if A is symmetric, then RA is an algebraic curvature tensor. This allows us to establish a simultaneous diagonalization result in the event that thre...

We have introduced a notion of C∗-symbolic dynamical system in [K. Matsumoto: Actions of symbolic dynamical systems on C∗-algebras, to appear in J. Reine Angew. Math.], that is a finite family of endomorphisms of a C∗-algebra with some conditions. The endomorphisms are indexed by symbols and yield both a subshift and a C∗-algebra of a Hilbert C∗-bimodule. The associated C∗-algebra with the C∗-s...

for all x, y£L. It is easily shown that every join-endomorphism is an isotone correspondence (i.e. x^y implies ®x=i 8y). It is also easy to see that the set / of antecedents of 0 under any join-endomorphism is an ideal. (For these and other facts used in the sequel we refer to the textbook of G. Birkhoff, Lattice theory, rev. ed., New York, 1948, henceforth cited as LT.) G. Birkhoff states in L...

In this paper we show that a generic polynomial p 2 C x 1 ; :::; x n ] of degree greater than n is a strong test polynomial for monomorphisms of C x 1 ; :::; x n ]: We give also examples of strong test polynomial in the class of all endomorphisms of C x 1 ; :::; x n ]: In particular we show that a generic polynomial p 2 C x; y] of degree greater than 3 is a strong test polynomial in the class o...