Crane and Frenkel proposed a notion of a Hopf category [2]. It was motivated by Lusztig’s approach to quantum groups – his theory of canonical bases. In particular, Lusztig obtains braided deformations Uqn+ of universal enveloping algebras Un+ for some nilpotent Lie algebras n+ together with canonical bases of these braided Hopf algebras [4, 5, 6]. The elements of the canonical basis are identi...

Crane and Frenkel proposed a notion of a Hopf category [2]. It was motivated by Lusztig’s approach to quantum groups – his theory of canonical bases. In particular, Lusztig obtains braided deformations Uqn+ of universal enveloping algebras Un+ for some nilpotent Lie algebras n+ together with canonical bases of these braided Hopf algebras [4, 5, 6]. The elements of the canonical basis are identi...

We present a comparative study of certain invariants defined for group actions and their analogues orbifolds. In particular, we prove that Fadell's equivariant category $G$-spaces coincides with the Lusternik-Schnirelmann orbifolds when is finite.

Let C be an abelian or exact category with enough projectives and let P be the full subcategory of projective objects of C . We consider the stable category C/P modulo projectives, as a left triangulated category [14], [36]. Then there is a triangulated category S(C/P) associated to C/P, which is universal in the following sense. There exists an exact functor S : C/P -t S(C/P) such that any exa...

Crane and Frenkel proposed a notion of a Hopf category [2]. It was motivated by Lusztig’s approach to quantum groups – his theory of canonical bases. In particular, Lusztig obtains braided deformations Uqn+ of universal enveloping algebras Un+ for some nilpotent Lie algebras n+ together with canonical bases of these braided Hopf algebras [4, 5, 6]. The elements of the canonical basis are identi...

We study the Farrell-Jones Conjecture with coefficients in an additive G-category with involution. This is a variant of the L-theoretic FarrellJones Conjecture which originally deals with group rings with the standard involution. We show that this formulation of the conjecture can be applied to crossed product rings R ∗ G equipped with twisted involutions and automatically implies the a priori ...

Customary empirical gravity models are parametric and rely on the assumption that exports from country i to j depend an additive index of three components: i-specific supply potential which is common across importers j; j-specific demand exporters i; bilateral trade frictions indexed by ij within in a generic period. We demonstrate data reject constancy these components category. The variation ...

We give a new geometric construction of the big projective module in the principal block of the BGG category O, or rather the corresponding D-module on the flag variety. Namely, given a one-parameter family of nondegenerate additive characters of the unipotent radical of a Borel subgroup which degenerate to the trivial character, there is a corresponding one-parameter family of Whittaker sheave...

The European Food Safety Authority (EFSA) received a request from the European Commission for authorisation of the product VevoVitall®, consisting of 99.9% benzoic acid in flaked form, to be used as a feed additive for pigs for fattening (category: zootechnical additives). EFSA was asked to deliver an opinion on the safety of VevoVitall® for the target animal, consumer, user and the environment...