Abstract We show that the image of a subshift X under various injective morphisms symbolic algebraic varieties over monoid universes with variety alphabets is finite type, respectively sofic subshift, if and only so . Similarly, let G be countable A , B Artinian modules ring. prove for every closed submodule $\Sigma \subset A^G$ -equivariant uniformly continuous module homomorphism $\tau \colon...

A graph property is a set of (countable) graphs. A homomorphism from a graph G to a graphH is an edge-preserving map from the vertex set of G into the vertex set of H; if such a map exists, we write G → H. Given any graph H, the hom-property →H is the set of H-colourable graphs, i.e., the set of all graphs G satisfying G → H. A graph property P is of finite character if, whenever we have that F...

A classical theorem of Burnside asserts that if X is a faithful complex character for the finite group G, then every irreducible character of G is a constituent of some power Xn of X . Fifty years after this appeared, Steinberg generalized it to a result on semigroup algebras K[G] with K an arbitrary field and with G a semigroup, finite or infinite. Five years later, Rieffel showed that the the...

We give a new geometric construction of the big projective module in the principal block of the BGG category O, or rather the corresponding D-module on the flag variety. Namely, given a one-parameter family of nondegenerate additive characters of the unipotent radical of a Borel subgroup which degenerate to the trivial character, there is a corresponding one-parameter family of Whittaker sheave...

We prove that over a commutative noetherian ring the three approaches to introducing depth for complexes: via Koszul homology, via Ext modules, and via local cohomology, all yield the same invariant. Using this result, we establish a far reaching generalization of the classical AuslanderBuchsbaum formula for the depth of finitely generated modules of finite projective dimension. We extend also ...

Contents 1. Introduction 1 2. Carlitz-Fermat quotients 2 3. Non-vanishing of Carlitz-Fermat quotients modulo primes 4 1. Introduction. Let q = p s , where p is a prime and s is a positive integer. Let F q be the finite field of q elements, and set A = F q [T ] and k = F q (T). Let τ be the mapping defined by τ (x) = x q , and let kτ denote the twisted polynomial ring. Let C : A → kτ (a → C a) b...

k field, algebraically closed G finite group Definitions (1) A representation of G over k of degree n is a homomorphism of groups ρ : G→GLn(k), or equivalently, a kG-module structure for an n-dimensional k vector space M , where kG is the group algebra. (2) A representation M is irreducible if it is a simple kG-module, and indecomposable if M 6= N1 ⊕ N2 for any non-trivial submodules N1, N2. No...

Given a compact manifold $M$ and $g\in C^{\infty}(M,U(l;\mathbb{C}))$ we construct Chern character $\mathrm{Ch}^-(g)$ which lives in the odd part of equivariant (entire) cyclic Chen-normalized bar complex $\underline{\mathscr{C}}(\Omega_{\mathbb{T}}(M\times \mathbb{T}))$ $M$, is mapped to Bismut-Chern under Chen integral map. It also shown that assignment $g\mapsto \mathrm{Ch}^-(g)$ induces wel...

Suppose that y is a continuous homomorphism of a locally compact group G into another such group, H, then ¡p induces in a natural way a homomorphism 9>* of the measure algebra of G, called M(G), into M(H). The action of <p* on the subspace M0(G) is studied in this paper. The space M0(G) is the nonabelian analogue to the space of measures on a locally compact abelian group whose Fourier-Stieltje...

We introduce the notion of “local system of ZT -twisted vertex operators” on a Z2-graded vector space M , generalizing the notion of local system of vertex operators [Li]. First, we prove that any local system of ZT -twisted vertex operators on M has a vertex superalgebra structure with an automorphism σ of order T with M as a σ-twisted module. Then we prove that for a vertex (operator) superal...