We study a class of $\mathbb{Z}^{d}$-substitution subshifts, including large family constant-length substitutions, and homomorphisms between them, i.e., factors modulo isomorphisms $\mathbb{Z}^{d}$. prove that any measurable factor even homomorphism associated to matrix commuting with the expansion matrix, induced continuous one. also get strong restrictions on normalizer group, proving endomor...

Let k be a field, C/k a proper, smooth, geometrically connected curve of genus g ≥ 1 given with a marked rational point 0 ∈ C(k), JC/k := Pic 0 C/k its Jacobian. Concretely, the group JC(k) is the group (under tensor product) of isomorphism classes of invertible sheaves L on C of degree zero. Given a point P ∈ C(k), we denote by I(P ) ⊂ OC the ideal sheaf of functions vanishing at P . Given P1,...

The aim of this note is to understand invertible modules over a commutative Salgebra in the sense of Elmendorf, Kriz, Mandell & May in some very well-behaved cases. Our main result shows that as long as the commutative S-algebra R has ‘reductions mod m’ for all maximal ideals m ⊳ R∗, and Noetherian localisations (R∗)m , then for every invertible R-module U , U∗ = π∗U is an invertible R∗-module.

We establish the algebraic reflexivity of three isometry groups of operator structures: The group of all surjective isometries on the unitary group, the group of all surjective isometries on the set of all positive invertible operators equipped with the Thompson metric, and the group of all surjective isometries on the general linear group of B(H), the operator algebra over a complex infinite d...

For a countable amenable group Γ and an element f in the integral group ring ZΓ being invertible in the group von Neumann algebra of Γ, we show that the entropy of the shift action of Γ on the Pontryagin dual of the quotient of ZΓ by its left ideal generated by f is the logarithm of the Fuglede-Kadison determinant of f . For the proof, we establish an `-version of Rufus Bowen’s definition of to...

It is known on the one hand that a Sturmian sequence can be generated geometrically by the intersections of a straight line with the unit grid in the plane, and on the other hand that fixed points of invertible substitutions are Sturmian. We give a new characterization of invertible substitutions, which allows to determine the straight line which generates the fixed point of a given invertible ...

The aim of this paper is to study a novel property of Boolean mappings called local intert-ibility. We focus on local invertibility of Boolean mappings which model ltering generators and study the case when ltering function is linear in the last variable.

The main result of this paper is a generalization the theorem Chevalley-Shephard-Todd to rings invariants pseudoreflection groups over Dedekind domains. In special case principal ideal domain in which group order invertible it proved that ring isomorphic polynomial ring. An intermediate every finitely generated regular graded algebra tensor product blowup algebras.

Let M be a compact Kähler manifold equipped with a Hamiltonian action of a compact Lie group G. In this paper, we study the geometric quantization of the symplectic quotient M/G. Guillemin and Sternberg [Invent. Math. 67 (1982), 515–538] have shown, under suitable regularity assumptions, that there is a natural invertible map between the quantum Hilbert space over M/G and the G-invariant subspa...