In this paper, it is shown that the category of stratified $L$-generalized convergence spaces is monoidal closed if the underlying truth-value table $L$ is a complete residuated lattice. In particular, if the underlying truth-value table $L$ is a complete Heyting Algebra, the Cartesian closedness of the category is recaptured by our result.

We introduce parabolic degenerations of rational Cherednik algebras of complex reflection groups, and use them to give necessary conditions for finite-dimensionality of an irreducible lowest weight module for the rational Cherednik algebra of a complex reflection group, and for the existence of a non-zero map between two standard modules. The latter condition reproduces and enhances, in the cas...

The level of a module over a differential graded algebra measures the number of steps required to build the module in an appropriate triangulated category. Based on this notion, we introduce a new homotopy invariant of spaces over a fixed space, called the level of a map. Moreover we provide a method to compute the invariant for spaces over a K-formal space. This enables us to determine the lev...

1.1. Setup. In this talk k is a field of characteristic 0. Let (W,S) be a Coxeter group with |S| = n < ∞. Also we let V = ∑ s∈S kes be the reflection representation of W , and R = k[V ]. R is a graded algebra with V ∗ in degree 2. We abbreviate M ⊗R N = MN for a right R-module M and a left R-module N . We let {αs}s∈S be the dual basis of {es}s∈S , which can be considered as elements in V ∗ ⊂ R....

let a be a banach algebra and x be a banach a-bimodule. in this paper, we dene a new product on a  x and generalize the module extension banach algebras. we obtain characterizations of arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new banach algebra.

Let g denote a reductive Lie algebra over an algebraically closed field of characteristic zero, and let I) denote a Cartan subalgebra of g. In this paper we study finitely generated g-modules that decompose into direct sums of finite dimensional l)-weight spaces. We show that the classification of irreducible modules in this category can be reduced to the classification of a certain class of ir...

in this paper we consider c0-group of unitary operators on a hilbert c*-module e. in particular we show that if a?l(e) be a c*-algebra including k(e) and ?t a c0-group of *-automorphisms on a, such that there is x?e with =1 and ?t (?x,x) = ?x,x t?r, then there is a c0-group ut of unitaries in l(e) such that ?t(a) = ut a ut*.

The faithful quasi-dual H and strict quasi-dual H ′ of an infinite braided Hopf algebra H are introduced and it is proved that every strict quasi-dual H ′ is an HHopf module. The connection between the integrals and the maximal rational Hsubmodule H of H is found. That is, H ∼= ∫ l H ⊗H is proved. The existence and uniqueness of integrals for braided Hopf algebras in the Yetter-Drinfeld categor...

We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i. e. for fusion categories), obtained recently in our joint work with D. Nikshych. In particular, we generalize to the categorical setting the Hopf and quasi-Hopf algebra freeness theorems due to Nichols–Zoeller and Schauenburg, respectively. We also gi...

In this paper we give a criterion for a left Gorenstein algebra to be AS-regular. Let A be a left Gorenstein algebra such that the trivial module Ak admits a finitely generated minimal free resolution. Then A is AS-regular if and only if its left Gorenstein index is equal to− inf{i |ExtA A (k, k)i = 0}. Furthermore, A is Koszul AS-regular if and only if its left Gorenstein index is depthAA = − ...