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...

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...

where Hom(π1(X), G) denotes the space of all group homomorphisms from the fundamental group π1(X) into G, and G acts on this space by conjugation. Let φ : π1(X) → G be a homomorphism, and let [φ] denote the corresponding point of LocG(X). Note that φ defines a π1(X)-module structure on g via the adjoint representation of G. Let us denote this π1(X)-module by gφ, and let Eφ denote the associated...

Every continuous map X → S defines, by composition, a homomorphism between the corresponding algebras of real-valued continuous functions C(S) → C(X). This paper deals with algebraic properties of the homomorphism C(S)→ C(X) in relation to topological properties of the map X → S. The main result of the paper states that a continuous map X → S between topological manifolds is a finite (branched)...

(c) μ(rs,m) = μ(r, μ(s,m)) (d) if 1 ∈ R, then μ(1,m) = m. We shall usually omit the notation of μ and simply write r ·m for μ(r,m). Thus axiom (c) would be written (rs) ·m = r · (s ·m), etc. Exercise 1. We denote by EndGrp(M) the set of group endomorphisms of M : An element φ ∈ EndGrp(M) is a group homomorphism φ : M → M . EndGrp(M) is naturally a ring, with addition and multiplication defined ...

Let G be the planar Galilean conformal algebra and G˜ its universal central extension. Then (resp. G˜) admits a triangular decomposition: G=G+?G0?G? G˜=G˜+?G˜0?G˜?). In this paper, we study generic Whittaker G-modules G˜-modules) of type ?, where ?:G+?G˜+?C is Lie homomorphism. We classify isomorphism classes modules. Moreover, show that module ? simple if only nonsingular. For nonsingular case...

Let [Formula: see text] be a commutative Noetherian ring. For finitely generated text]-module text], Northcott introduced the reducibility index of which is number submodules appearing in an irredundant irreducible decomposition submodule text]. On other hand, for Artinian Macdonald proved that sum-irreducible representation does not depend on choice representation. This called sum-reducibility...

We show that in a triangulated category, the existence of a cluster tilting object often implies that the homomorphism groups are bounded in size. This holds for the stable module category of a selfinjective algebra, and as a corollary we recover a theorem of Erdmann and Holm. We then apply our result to Calabi-Yau triangulated categories, in particular stable categories of maximal Cohen-Macaul...