We prove that, for every compact Kähler manifold, the period map of its Kuranishi family is induced by a natural L∞-morphism. This implies, by standard facts about L∞-algebras, that the period map is a “morphism of deformation theories” and then commutes with all deformation theoretic constructions (e.g. obstructions).

We give a formula for a morphism between Specht modules over (Z/m)Sn, where n ≥ 1, and where the partition indexing the target Specht module arises from that indexing the source Specht module by a downwards shift of one box, m being the box shift length. Our morphism can be reinterpreted integrally as an extension of order m of the corresponding Specht lattices.

We define generalizations of the Albanese variety for a projective variety X. The generalized Albanese morphisms X albr // _ _ _ Albr(X) contract those curves C in X for which the induced morphism Hom(π1(X),U(r)) → Hom(π1(C),U(r)) has a finite image. Thus, they may be interpreted as a U(r)-version of the Shafarevich morphism.

Let G be a connected reductive affine algebraic group defined over the complex numbers, and K ⊂ G be a maximal compact subgroup. Let X, Y be irreducible smooth complex projective varieties and f : X → Y an algebraic morphism, such that π1(Y ) is virtually nilpotent and the homomorphism f∗ : π1(X)→ π1(Y ) is surjective. Define R ( π1(X), G ) = {ρ ∈ Hom ( π1(X), G ) | A ◦ ρ factors through f∗} , ...

In a reputation-based trust management system an entity’s behaviour determines its reputation which in turn affects other entities interaction with it. We present a mathematical model for trust aimed at global computing environments which, as opposed to many traditional trust management systems, supports the dynamics of reputationbased systems in the sense that trusting relationships are monito...

The primary aim of this work is to study the compositional characterization of multipartite quantum states in an abstract setting of commutative Frobenius algebras expressed internal to symmetric monoidal categories. This work is based on the compositional structure of multipartite quantum entanglement established by Bob Coecke and Aleks Kissinger in [11]. The two SLOCC classes of tripartite en...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

Mossé proved that primitive morphisms are recognizable. In this paper we give a computable upper bound for the constant of recognizability of such a morphism. This bound can be expressed only using the cardinality of the alphabet and the length of the longest image under the morphism of a letter.

We find an explicit closed form for the subword complexity of the infinite fixed point of the morphism sending a → aab and b → b. This morphism is then generalized in three different ways, and we find similar explicit expressions for the subword complexity of the generalizations.

In the study of pre-Lie algebras, concept pre-morphism arises naturally as a generalization standard notion morphism. Pre-morphisms can be defined for arbitrary (not-necessarily associative) algebras over any commutative ring k with identity, and dualized in various ways to generalized morphisms (related pre-Jordan algebras) anti-pre-morphisms anti-pre-Lie algebras). We consider idempotent pre-...