x⊗ f(t), y ⊗ g(t) 7→ −κ(x, y) · Rest=0 fdg. Denote by ĝκ–mod the category of ĝκ-modules which are discrete, i.e., any vector is annihilated by the Lie subalgebra g ⊗ tC[[t]] for sufficiently large N ≥ 0, and on which 1 ∈ C ⊂ ĝκ acts as the identity. We will refer to objects of these category as modules at level κ. Let GrG = G((t))/G[[t]] be the affine Grassmannian of G. For each κ there is a ca...

Let k be an algebraically closed field and let T be the k-linear algebraic triangulated category generated by a w-spherical object for an integer w. For certain values of w this category is classical. For instance, if w = 0 then it is the compact derived category of the dual numbers over k. As main results of the paper we show that for w ≤ 0, the category T has no non-trivial t-structures, but ...

Let T be the functor on the category of unstable algebras over the Steenrod algebra constructed by Lannes. We use an argument involving Kähler differentials to show that T preserves polynomial algebras. This leads to new and relatively simple proofs of some topological and algebraic theorems. §

Transactional graph transformation systems (t-gtss) have been recently proposed as a mild extension of the standard dpo approach to graph transformation, equipping it with a suitable notion of atomic execution for computations. A typing mechanism induces a distinction between stable and unstable items, and a transaction is defined as a shift-equivalence class of computations such that the start...

In this paper, we define the new notion of quasi-prime ideal which generalizes at once both prime ideal and primary ideal notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which admits the Zariski topology as a subspace topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is pro...

Containers [1] are an elegant representation of a wide class of datatypes in terms of shapes and positions in shapes. In our FoSSaCS 2012 work [2], we introduced directed containers as a special case to account for the common situation where every position in a shape determines another shape, informally the subshape rooted by that position; some examples being the datatypes of nonempty lists an...

In this paper we will try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should has.

The main purpose of this paper is to introduce the concept of general Γ-hypermodules as a generalization of Γ-hypermodules, as a generalization of Γ-modules and as a generalization of modules. Then we extended the isomorphism theorems to general Γhypermodules. Also, it is observer that if N is a normal Γ-subhypermodule of Γ-hypermodule M, then, [M : N∗] is an abelian group. Finally, we show tha...