Related papers: Coaction functors, II

In this paper we set up the foundations around the notions of formal differentiation and formal integration in the context of commutative Hopf algebroids and Lie-Rinehart algebras. Specifically, we construct a contravariant functor from the…

We introduce the notion of joint torsion for several commuting operators satisfying a Fredholm condition. This new secondary invariant takes values in the group of invertibles of a field. It is constructed by comparing determinants…

In this paper we introduce and investigate the notion of semiseparable functor. One of its first features is that it allows a novel description of separable and naturally full functors in terms of faithful and full functors, respectively.…

In the first part of the paper, we develop a theory of crossed products of a $C^*$-algebra $A$ by an arbitrary (not necessarily extendible) endomorphism $\alpha:A\to A$. We consider relative crossed products $C^*(A,\alpha;J)$ where $J$ is…

We give, for a complex algebraic variety $S$, a Hodge realization functor $\mathcal F_S^{Hdg}$ from the derived category of constructible motives $DA_c(S)$ to the derived category $D(MHM(S))$ of algebraic mixed Hodge modules over $S$.…

In this paper, we show that every pair of absolutely compatible Hilbert space effects are coexistent and exhibit a partial orthogonality property. We introduce the notion of partially ortho-coexistence. We generalize absolute compatibility…

We investigate properties of commutative subrings and ideals in non-commutative algebraic crossed products for actions by arbitrary groups. A description of the commutant of the base coefficient subring in the crossed product ring is given.…

We study compatible actions (introduced by Brown and Loday in their work on the non-abelian tensor product of groups) in the category of Lie algebras over a fixed ring. We describe the Peiffer product via a new diagrammatic approach, which…

Let $k$ be a regular ring, and let $A,B$ be essentially finite type $k$-algebras. For any functor $F:{D}(A)\times\dots\times{D}(A)\to{D}(B)$ between their derived categories, we define its twist…

We investigate the coefficients generated by expressing the falling factorial $(xy)_k$ as a linear combination of falling factorial products $(x)_l (y)_m$ for $l,m =1,...,k$. Algebraic and combinatoric properties of these coefficients are…

We introduce generalized Frobenius-Schur indicators for pivotal categories. In a spherical fusion category C, an equivariant indicator of an object in C is defined as a functional on the Grothendieck algebra of the quantum double Z(C) via…

This note studies the behavior of Euler characteristics and of intersection homology Euler characterstics under proper morphisms of algebraic (or analytic) varieties. The methods also yield, for algebraic (or analytic) varieties, formulae…

Let P be a semigroup that admits an embedding into a group G. Assume that the embedding satisfies a certain Toeplitz condition and that the Baum-Connes conjecture holds for G. We prove a formula describing the K- theory of the reduced…

Exponentiable functors between quantaloid-enriched categories are characterized in elementary terms. The proof goes as follows: the elementary conditions on a given functor translate into existence statements for certain adjoints that obey…

We provide a construction of the fixed points of functors which may not be inital algebras or final coalgebras. For an endofunctor F, this fixed point construction may be expressed as a pair of adjoint functors between F-coalgebras and…

In this paper, we introduce and study the persistent approximation property for quantitative K-theory of filtered C*-algebras. In the case of crossed product C*-algebras, the persistent approximation property follows from the Baum-Connes…

Let G be a compact Lie group. Let E be a principal G-bundle over a closed manifold M, and Ad(E) its adjoint bundle. In this paper we describe a new Frobenius algebra structure on h_*(Ad(E)), where h_* is an appropriate generalized homology…

We define universal factorial Schur $P,Q$-functions and their duals, which specialize to generalized (co)-homology "Schubert basis" for loop spaces of the classical groups. We also investigate some of their properties.

The purpose of this paper is to show how a congruence between (the Fourier coefficients of) a Hilbert cusp form and a Hilbert Eisenstein series of parallel weight $2$ gives rise to congruences between algebraic parts of critical values of…

We consider two categories of C*-algebras; in the first, the isomorphisms are ordinary isomorphisms, and in the second, the isomorphisms are Morita equivalences. We show how these two categories, and categories of dynamical systems based on…