Related papers: Higher limits over the fusion orbit category

Let $\G$ be a semisimple algebraic group defined over a number field $K$, $\te$ a maximal $K$-split torus of $\G$, $\mathcal{S}$ a finite set of valuations of $K$ containing the archimedean ones, $\OO$ the ring of $\mathcal{S}$-integers of…

We define for a topological group G and a family of subgroups F two versions for the classifying space for the family F, the G-CW-version E_F(G) and the numerable G-space version J_F(G). They agree if G is discrete, or if G is a Lie group…

Let $\mathscr {C}(G,H,\psi)$ be a finite group scheme-theoretical category over an algebraically closed field of characteristic $p\ge 0$ as introduced by the first author. For any indecomposable exact module category over $\mathscr…

For a group $G$ and a subgroup $H$ of $G$ this article discusses the normalizer of $H$ in the units of a group ring $RG$. We prove that $H$ is only normalized by the `obvious' units, namely products of elements of $G$ normalizing $H$ and…

Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module of finite dimension. If G/H \subset P(V) is a spherical orbit and if X is its closure,…

For any finite group $G$, any transitive $G$-set $X$ and any field ${\Bbb F}$, we consider the vector space ${\Bbb F}^X$ of all functions from $X$ to ${\Bbb F}$, which is a $G$-space isomorphic to the permutation ${\Bbb F} G$-module ${\Bbb…

It is well-known that the existence of more than two ends in the sense of J.R. Stallings for a finitely generated discrete group $G$ can be detected on the cohomology group $\mathrm{H}^1(G,R[G])$, where $R$ is either a finite field, the…

It is well-known that the Harish-Chandra transform, $f\mapsto\mathcal{H}f,$ is a topological isomorphism of the spherical (Schwartz) convolution algebra $\mathcal{C}^{p}(G//K)$ (where $K$ is a maximal compact subgroup of any arbitrarily…

Let $G$ be a residually finite, good group of finite virtual cohomological dimension. We prove that the natural monomorphism $G\hookrightarrow\hat{G}$ induces a bijective correspondence between conjugacy classes of finite $p$-subgroups of…

Given an extension $0\to V\to G\to Q\to1$ of locally compact groups, with $V$ abelian, and a compatible essentially bijective $1$-cocycle $\eta\colon Q\to\hat V$, we define a dual unitary $2$-cocycle on $G$ and show that the associated…

According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup D of a compact abelian group G determines G if the restriction homomorphism G^ --> D^ of the dual groups is a topological isomorphism. We introduce four conditions on D…

Let $G$ be a locally compact group. Consider the C$^*$-algebra $C_0(G)$ of continuous complex functions on $G$, tending to 0 at infinity. The product in $G$ gives rise to a coproduct $\Delta_G$ on the C$^*$-algebra $C_0(G)$. A locally…

We study three restrictions on normalizers or centralizers in finite p-groups, namely: (i) |N_G(H) : H| <= p^k for every H non-normal in G, (ii) |N_G(<g>) : <g>| <= p^k for every <g> non-normal in G, and (iii) |C_G(g) : <g>| <= p^k for…

Let G be a connected and reductive algebraic group over an algebraically closed field of characteristic p > 0. An interesting class of representations of G consists of those G-modules having a good filtration -- i.e. a filtration whose…

Let F be a non-Archimedean locally compact field of residue characteristic p, let D be a finite dimensional central division F-algebra and let R be an algebraically closed field of characteristic different from p. To any irreducible smooth…

Let $\mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $k$ its residual field, $\mathcal{P}$ a proper smooth formal scheme over $\mathcal{V}$, $P$ its special fiber, $T$ a divisor of $P$, $U:=P\setminus T$, $Y$ a…

Let F be a non Archimedean locally compact field of residue characteristic different from 2, let G be a connected reductive group defined over F, let s be an involutive F-automorphism of G and H an open F-subgroup of the fixed points group…

We propose a framework for fusion category symmetry on the (1+1)D lattice in the infinite-volume limit by giving a formal interpretation of SymTFT decompositions. Our approach is based on axiomatizing physical boundary subalgebra of…

In this paper we extend categorically the notion of a finite nilpotent group to fusion categories. To this end, we first analyze the trivial component of the universal grading of a fusion category C, and then introduce the upper central…

A discrete DJS-hypergroup is constructed in connection with the linearization formula for the product of two spherical elements for a quantum Gelfand pair of two compact quantum groups. A similar construction is discussed for the case of a…