Finite additive cellular automata with fixed and periodic boundary conditions are considered as endomorphisms over pattern spaces. A characterization of the nilpotent and regular parts of these endomorphisms is given in terms of their minimal polynomials. Generalized eigenspace decomposition is determined and relevant cyclic subspaces are described in terms of symmetries. As an application, the...

Previously, we have shown that the CAR algebra for fermions is embedded in the Cuntz algebra O2 in such a way that the generators are expressed in terms of polynomials in the canonical generators of the latter, and it coincides with the U(1)-fixed point subalgebra A ≡ O 2 of O2 for the canonical gauge action. Based on this embedding formula, some properties of A are studied in detail by restric...

algebra and enumerative combinatorics We learn something when we can interpret combinatorial numbers as orders of algebraic structures, especially groups. Lagrange’s Theorem means that group orders tend to have a rich arithmetic structure. I first learned from Norman’s paper on chip-firing games the fact that the number of spanning trees of a graph is the order of an abelian group canonically a...

In this paper, we initiate the study of endomorphisms and modular theory of the graph C*-algebras Oθ of a 2-graph F + θ on a single vertex. We prove that there is a semigroup isomorphism between unital endomorphisms of Oθ and its unitary pairs with a twisted property. We characterize when endomorphisms preserve the fixed point algebra F of the gauge automorphisms and its canonical masa D. Some ...

We give a detailed account of the use of Q-curve reductions to construct elliptic curves over Fp2 with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the same way as Gallant–Lambert–Vanstone (GLV) and Galbraith–Lin–Scott (GLS) endomorphisms. Like GLS (which is a degenerate case of our construction), we offer the advantage over GLV of ...

1. Introduction Groups for which the distributively generated near-ring generated by the endomorphisms is in fact a ring are known as U-groups and are discussed in (3). R. Faudree in (1) has given the only published examples of non-abelian JS-groups by presenting defining relations for a family of p-groups. However, as shown in (3), Faudree's group does not have the desired property when p = 2....