Let M be a finite monoid of Lie type (these are the finite analogues of linear algebraic monoids) with group of units G . The multiplicative semigroup ^AfF), where F is a finite field, is a particular example. Using HarishChandra's theory of cuspidal representations of finite groups of Lie type, we show that every complex representation of M is completely reducible. Using this we characterize t...

Anumerical semigroup is a subset ofN containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of algebraic geometry codes, Weierstrass semigroups are crucial for defining bounds on the minimum distance as well as for defining improvements on the dimension of codes...

The conservativity of a minimal quantum dynamical semigroup is proved whenever there exists a " reference " subharmonic operator bounded from below by the dissipative part of the infinitesimal generator. We discuss applications of this criteria in mathematical physics and quantum probability. 1. Introduction A quantum dynamical semigroup (q.d.s.) T = (T t) t≥0 on B(h), the Banach space of bound...

We deal with the maximal bifix code construction which is a natural generalization of a group code construction. For a surjective morphism from a free monoidA∗ onto a completely simple semigroup with an adjoined identityM(G; I, J ; )1 and a submonoid S of M(G; I, J ; )1, under certain conditions, the base of a submonoid −1(S) is a maximal bifix code X. We investigate the relationships between t...

Let’s begin by recalling a fact about 2d conformal field theories from Phil’s talk last week. Firstly, we can define a complex semigroup A whose objects are conformal equivalence classes of Riemann surfaces which are diffeomorphic to annuli, equipped with parameterisations of their boundary components, one incoming and one outgoing. The semigroup operation is given by gluing an outgoing to an i...

We present a simple approach to study the one–dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space P2(R) of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of “sticky” particles, we obtain new explicit estimates of the solution in terms of the initial mass and momentum and we are able to construct an evolutio...

In any semigroup S, we say that elements a and b are left inverses of each other if a = aba, b = bab and a L b, in which case we write a γ b. Right inverses are defined dually with the notation δ. Set τ = δγ. We study the classes of semigroups in which τ has some of the usual properties of a relation. We also consider properties of (maximal) completely simple subsemigroups of S. In terms of the...

Suppose X={Xt,t≥0} is a supercritical superprocess. Let ϕ be the non-negative eigenfunction of mean semigroup X corresponding to principal eigenvalue λ>0. Then Mt(ϕ)=e−λt〈ϕ,Xt〉,t≥0, martingale with almost sure limit M∞(ϕ). In this paper we study rate at which Mt(ϕ)−M∞(ϕ) converges 0 as t→∞ when process may not have finite variance. Under some conditions on semigroup, provide sufficient and nece...

Let G be a torsion-free abelian group of type (0, 0, 0, . . . ) and R an integrally closed integral domain with quotient field K. We show that every divisorial ideal (respectively, t-ideal) J of the group ring R[X;G] is of the form J = hIR[X;G] for some h ∈ K[X;G] and a divisorial ideal (respectively, t-ideal) I of R. Consequently, there are natural monoid isomorphisms Cl(R) ∼= Cl(R[X;G]) and C...

Given the infinitesimal generator A of a C0-semigroup on the Banach space X which satisfies the Kreiss resolvent condition, i.e., there exists an M > 0 such that ‖(sI−A)‖ ≤ M Re(s) for all complex s with positive real part. We show that for general Banach spaces this condition does not give any information on the growth of the associated C0-semigroup. For Hilbert spaces the situation is less dr...