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This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…

Let $A$ be a finite or countable alphabet and let $\theta$ be literal (anti)morphism onto $A^*$ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…

Let G/H be a hyperbolic space over R C or H, and let K be a maximal compact subgroup of G. Let D denote a certain explicit invariant differential operator, such that the non-cuspidal discrete series belong to the kernel of D. For any…

Let $\mathcal A$ be a Banach algebra for which the group of invertible elements is connected. A subspace $\mathcal L \subseteq \mathcal A$ is a Lie ideal in $\mathcal A$ if, and only if, it is invariant under inner automorphisms. This…

Left invariant affine structures in a Lie group $G$ are in one-to-one correspondence with left-symmetric algebras over its Lie algebra $\mathfrak g=T_eG$ (``over'' means that the commutator $[x,y]=xy-yx$ coincides with the Lie bracket;…

Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…

Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…

These notes are inspired by the theory of cellular automata. A linear cellular automaton on a lattice of finite rank or on a toric grid is a discrete dinamical system generated by a convolution operator with kernel concentrated in the…

We consider a family of dynamical systems (A,alpha,L) in which alpha is an endomorphism of a C*-algebra A and L is a transfer operator for \alpha. We extend Exel's construction of a crossed product to cover non-unital algebras A, and show…

Cellular automata (CA) consist of an array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global…

For an arbitrary group $G$ and arbitrary set $A$, we define a monoid structure on the set of all uniformly continuous functions $A^G\to A$ and then we show that it is naturally isomorphic to the monoid of cellular automata $\mathrm{CA}(G,…

Given a finite set $A$ and a group homomorphism $\phi : H \to G$, a $\phi$-cellular automaton is a function $\mathcal{T} : A^G \to A^H$ that is continuous with respect to the prodiscrete topologies and $\phi$-equivariant in the sense that…

A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to unfold the concept of conditional predictability for systems whose trajectory can only be piecewise known. The…

A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space $\mathcal{H}$ is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group $G$ on…

To any Hamiltonian action of a reductive algebraic group $G$ on a smooth irreducible symplectic variety $X$ we associate certain combinatorial invariants: Cartan space, Weyl group, weight and root lattices. For cotangent bundles our…

We study the invariant algebraic D-modules on an affine variety under the action of an algebraic group.For linear algebraic groups with the multiplication action by themselves, such D-modules correspond to representations of their Lie…

We call a unital locally convex algebra $A$ a continuous inverse algebra if its unit group $A^\times$ is open and inversion is a continuous map. For any smooth action of a, possibly infinite-dimensional, connected Lie group $G$ on a…

Let $A$ be a connected commutative $\C$-algebra with derivation $D$, $G$ a finite linear automorphism group of $A$ which preserves $D$, and $R=A^G$ the fixed point subalgebra of $A$ under the action of $G$. We show that if $A$ is generated…

Quantum general relativity may be considered as generally covariant QFT on differentiable manifolds, without any a priori metric structure. The kinematically covariance group acts by general diffeomorphisms on the manifold and by…

We study reversible quantum cellular automata with the restriction that these are also Clifford operations. This means that tensor products of Pauli operators (or discrete Weyl operators) are mapped to tensor products of Pauli operators.…