In this paper we give a construction of algebraic (Artin) stacks Pd,g,n endowed with a modular map onto the moduli stack of pointed stable curves Mg,n, for g ≥ 3. The stacks Pd,g,n are smooth, irreducible and have dimension 4g − 3+n. They yield a geometrically meaningful compactification of the degree d universal Picard stack over Mg,n, parametrizing n-pointed smooth curves together with a degr...

Let S be a (discrete) semigroup, and let ` (S) be the Banach algebra which is the semigroup algebra of S. We shall study the structure of this Banach algebra and of its second dual. We shall determine exactly when ` (S) is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are ‘forbidden values’ for this constant. The second dual of ` (S) is the Banach ...

Let S be a semigroup, and let ` (S) be the Banach algebra which is the semigroup algebra of S. We shall study the structure of this Banach algebra and of its second dual. We shall determine exactly when ` (S) is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are ‘forbidden values’ for this constant. The second dual of ` (S) is the Banach algebraM(βS...

We calculate the production rates of the second Kaluza-Klein (KK) photon γ(2) and Z boson Z(2) at the LHC including all significant processes in the minimal universal extra dimension (MUED) model. For discrimination of the MUED model from other TeV scale models in hadron collider experiments, γ(2) and Z(2) play a crucial role. In order to discuss the discrimination and calculate their productio...

We introduce a concept and develop a theory of Galois subalgebras in skew semigroup rings. Proposed approach has a strong impact on the representation theory, first of all the theory of Harish-Chandra modules, of many infinite dimensional algebras including the Generalized Weyl algebras, the universal enveloping algebras of reductive Lie algebras, their quantizations, Yangians etc. In particula...

For any C∗-algebra A, an A-dynamical system is a C∗-dynamical system that contains A and can be generated by the images of A under the semigroup of nonnegative time endomorphisms. There is a universal Adynamical system that occupies a position in noncommutative dynamics that resembles the position of the tangent bundle in commutative dynamics. We describe an approach to noncommutative dilation ...

We show that a certain moduli space of minimal A∞ -structures coincides with the modular compactification M1,n(n− 1) of M1,n constructed by Smyth in [22]. In addition, we describe these moduli spaces and the universal curves over them by explicit equations, prove that they are normal and Gorenstein, show that their Picard groups have no torsion and that they have rational singularities if and o...

The moduli space of smooth curves admits a beautiful compactification Mg,n ⊂ Mg,n by the moduli space of stable curves. In this paper, we undertake a systematic classification of alternate modular compactifications ofMg,n. Let Ug,n be the (non-separated) moduli stack of all n-pointed connected reduced one-dimensional schemes of arithmetic genus g. When g = 0, U0,n is irreducible and we classify...

An inverse semigroup is a semigroup S such that for each x e S there exists a unique inverse x~ & S such that both xx~x=x and x~xx~=x~\ This condition is equivalent to S both being (von Neumann) regular and having all idempotents commute. The classic example of such a semigroup is the symmetric inverse semigroup Ix of all partial bijections on a set X under the standard composition of partial f...

Let G be a locally compact group, and consider the weakly-almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C∗-subalgebra of the commutative C∗-algebra M(G)∗, and so has character space, say K. In this paper, we investigate properties of K. We present two proofs, one using tensor product techniques, and the other using vector-valued integration, to s...