Related papers: Operations on A-theoretic nil-terms

We show that a compact rigid balanced braided monoidal category with enough compact projective objects gives rise to a system of mapping class group representations compatible with the gluing along marked intervals. A motivation to consider…

We propose a notion of Frobenius-Perron dimension for certain free $\mathbb{Z}$-modules of infinite rank and compute it for the $\mathbb{Z}$-modules of finite dimensional complex representations of unitary groups with nonnegative dominant…

We construct a separable Frobenius monoidal functor from $\mathcal{Z}\big(\mathsf{Vect}_H^{\omega|_H}\big)$ to $\mathcal{Z}\big(\mathsf{Vect}_G^\omega\big)$ for any subgroup $H$ of $G$ which preserves braiding and ribbon structure. As an…

The stable category of modules over the algebra of a finite group with coefficients in a field is a compactly generated tensor triangulated category, that has been studied extensively in representation theory. In this paper, we provide a…

In "Frobenius Categories versus Brauer Blocks" and in "Ordinary Grothendieck groups of a Frobenius P-category" we consider suitable inverse limits of Grothendieck groups of categories of modules in characteristics p and zero, obtained from…

In this paper we identify the ``nil-terms'' for Waldhausen's algebraic K-theory of spaces functor as the reduced K-theory of a category of equivariant spaces equipped with a homotopically nilpotent endomorphism.

For M and N finite module categories over a finite tensor category C, the category Rex_C(M,N) of right exact module functors is a finite module category over the Drinfeld center Z(C). We study the internal Homs of this module category,…

In this paper we construct an "abstract Fock space" for general Lie types that serves as a generalisation of the infinite wedge $q$-Fock space familiar in type $A$. Specifically, for each positive integer $\ell$, we define a…

By finite quantum groups we mean Lusztig's finite-dimensional pointed Hopf algebras called quantum Frobenius Kernels [9, 10], and their natural generalizations due to Andruskiewitsch and Schneider [2, 3]. For a Hopf algebra $H$ in a special…

We survey some aspects of Frobenius algebras, Frobenius structures and their relation to finite Hopf algebras using graphical calculus. We focus on the `yanking' moves coming from a closed structure in a rigid monoidal category, the…

For any finite-dimensional factorizable ribbon Hopf algebra H and any ribbon automorphism omega of H, we establish the existence of the following structure: an H-bimodule F_omega and a bimodule morphism Z_omega from Lyubashenko's Hopf…

Let H be a Hopf algebra and A an H-simple right H-comodule algebra. It is shown that under certain hypotheses every (H,A)-Hopf module is either projective or free as an A-module and A is either a quasi-Frobenius or a semisimple ring. As an…

Higher Homotopy van Kampen Theorems allow the computation as colimits of certain homotopical invariants of glued spaces. One corollary is to describe homotopical excision in critical dimensions in terms of induced modules and crossed…

We identify additional structure on a conservative lax monoidal functor from a closed monoidal category $\mathcal{C}$ to a Grothendieck-Verdier category $\mathcal{D}$, such that the Grothendieck-Verdier structure of $\mathcal{D}$ lifts to…

Given a complex manifold endowed with a $\mathbb{C}^\times$-action and a DQ-algebra equipped with a compatible holomorphic Frobenius action (F-action), we prove that if the $\mathbb{C}^\times$-action is free and proper, then the category of…

In this note, we extend the inductions and restrictions of modules over finite groups to non-injective group homomorphisms, establishing transitivity, Frobenius reciprocity, Mackey's formula, etc.

In this paper we develop the theory of operads, algebras and modules in cofibrantly generated symmetric monoidal model categories. We give J-semi model strucures, which are a slightly weaker version of model structures, for operads and…

The paper studies the dimensions of irreducible components of commuting varieties of (restricted) nilpotent $r$-tuples in a classical Lie algebra $\mathfrak{g}$ defined over an algebraically closed field $k$. As applications, we obtain some…

For a finite dimensional semisimple Lie algebra and a root of unity, Lusztig defined an infinite dimensional quantum group of divided powers. Under certain restrictions on the order of the root of unity, he constructed a Frobenius…

We prove several results about p-divisible groups and Rapoport-Zink spaces. Our main goal is to prove that Rapoport-Zink spaces at infinite level are naturally perfectoid spaces, and to give a description of these spaces purely in terms of…