For G a finite abelian group, we study the properties of general equivalence relations on Gn = Gn Sn , the wreath product of G with the symmetric group Sn , also known as the G-coloured symmetric group. We show that under certain conditions, some equivalence relations give rise to subalgebras of kGn as well as graded connected Hopf subalgebras of ⊕ n≥o kGn . In particular we construct a G-colou...

In m odel-based testing the behavior of a system u n d er test is com pared autom atically w ith the behavior of a model. A significant fraction of issues found in testing appear to be caused by m istakes in the model. In o rd e r to ensure th a t it prescribes the desired behavior, it has to be validated by a hum an. In this w ork we describe a tool, esm V iz, to support this validation. M ode...

intimately connected with duality theory (the notation is that of [1]). In both cases the middle algebra is the closure of L(G) in the dual of the first algebra and also the predual of the third algebra (at least when G is amenable in the second case). Furthermore, the third algebra is closely connected with the multiplier algebra of the first algebra. For abelian groups, compact or discrete, V...

Let g be a Lie algebra over a field k of characteristic zero, and a fix positive integer N. The Lie algebra ĝ = g ⊗k k[t]/t N+1 k[t] is called a truncated current Lie algebra. In this paper a highest-weight theory for ĝ is developed when the underlying Lie algebra g possesses a triangular decomposition. The principal result is the reducibility criterion for the Verma modules of ĝ for a wide cla...

Let R be monomial sub-algebra of k[x1, . . . , xN ] generated by square free monomials of degree two. This paper addresses the following question: when is R a complete intersection? For such a k-algebra we can associate a graph G whose vertices are x1, . . . , xN and whose edges are {(xi, xj)|xixj ∈ R}. Conversely, for any graph G with vertices {x1, . . . , xN} we define the edge algebra associ...

Let g be a finite dimensional simple Lie algebra over the complex numbers C. Consider the exterior algebra R := ∧ (g⊕ g) on two copies of g. Then, the algebra R is bigraded under R = ∧p(g)⊗∧q(g). The diagonal adjoint action of g gives rise to a g-algebra structure on R compatible with the bigrading. There are three ‘standard’ copies of the adjoint representation g in R. Let J be the (bigraded) ...

The Cuntz algebra carries in a natural way the structure of a module algebra over the quantized universal enveloping algebra Uq(g), and the structure of a co-module algebra over the quantum group Gq associated with Uq(g). These two algebraic structures are dual to each other via the duality between Gq and Uq(g).

Let G be a locally compact Abelian group; I’ the dual group of G; CO(l_’)the algebra of continuous functions on r which vanish at infinity; CB(17)the continuous, bounded functions on r; M(G) the algebra of bounded Borel measures on G; Ll(G) the algebra of absolutely continuous measures; and M(G)A the algebra of l?ourier-Stielt jes transforms. Let E denote a compact subset of I’, and let A(E) be...

This paper describes Gammall og, a logic language based on multiset rewriting. The language combines the ability of describing parallel programs made of multiset transformation rules as in GAMMA with the execution model of logic programming in a strongly typed framework as in GG odel. We describe the design choices, the syntax and the semantics. Gammall og provides a standard model theoretic se...