We propose a generalisation of Exel’s crossed product by a single endomorphism and a transfer operator to the case of actions of abelian semigroups of endomorphisms and associated transfer operators. The motivating example for our definition yields new crossed products, not obviously covered by familiar theory. Our technical machinery builds on Fowler’s theory of Toeplitz and Cuntz-Pimsner alge...

We prove the Zariski dense orbit conjecture in positive characteristic for endomorphisms of G a N defined over F p ‾ .

We construct new families of elliptic curves over Fp2 with efficiently computable endomorphisms, which can be used to accelerate elliptic curvebased cryptosystems in the sameway asGallant–Lambert–Vanstone (GLV) and Galbraith–Lin–Scott (GLS) endomorphisms. Our construction is based on reducingQ-curves—curves over quadratic number fields without complex multiplication, butwith isogenies to their ...

Based on an embedding formula of the CAR algebra into the Cuntz algebra O2p , properties of the CAR algebra are studied in detail by restricting those of the Cuntz algebra. Various ∗-endomorphisms of the Cuntz algebra are explicitly constructed, and transcribed into those of the CAR algebra. In particular, a set of ∗-endomorphisms of the CAR algebra into its even subalgebra are constructed. Acc...

We construct new families of elliptic curves over Fp2 with efficiently computable endomorphisms, which can be used to accelerate elliptic curvebased cryptosystems in the same way as Gallant–Lambert–Vanstone (GLV) and Galbraith–Lin–Scott (GLS) endomorphisms. Our construction is based on reducing Q-curves—curves over quadratic number fields without complex multiplication, but with isogenies to th...

A ring or an idempotent semiring is associative provided that additive endomorphisms are multiplicative.

We study some dynamical properties of skew products of Hénon maps of C2 that are fibered over a compact metric space M . The problem reduces to understanding the dynamical behavior of the composition of a pseudorandom sequence of Hénon mappings. In analogy with the dynamics of the iterates of a single Hénon map, it is possible to construct fibered Green functions that satisfy suitable invarianc...

We classify endomorphisms of the plane that preserve a pencil of curves.