Related papers: Beyond a question of Markus Linckelmann

The goal of this paper is to classify fusion categories $\otimes$-generated by a $K$-normal object (defined in this paper) of Frobenius-Perron dimension less than 2. This classification has recently become accessible due to a result of…

Let X be a non-compact Calabi-Yau manifold and f be a holomorphic function on X with compact critical locus. We introduce the notion of f-twisted Sobolev spaces for the pair (X,f) and prove the corresponding Hodge-to-de Rham degeneration…

In "Frobenius Categories versus Brauer Blocks", Progress in Math. 274, we introduce the Frobenius P-categories giving two quite different definitions of them. In this paper, we exhibit a third equivalent definition based on the form of the…

We disprove a strong form of the Regular Inverse Galois Problem: there exist finite groups $G$ which do not have a realization $F/\Qq(T)$ that induces all Galois extensions $L/\Qq(U)$ of group $G$ by specializing $T$ to $f(U) \in \Qq(U)$.…

Consider a Frobenius kernel G in a split semisimple algebraic group, in very good characteristic. We provide an analysis of support for the Drinfeld center Z(rep(G)) of the representation category for G, or equivalently for the…

Glauberman's $Z^*$-theorem and analogous statements for odd primes show that, for any prime $p$ and any finite group $G$ with Sylow $p$-subgroup $S$, the centre of $G/O_{p^\prime}(G)$ is determined by the fusion system $\mathcal{F}_S(G)$.…

This article introduces and provides the mathematical foundation of the open string Floer theory of Landau-Ginzburg model viaWitten equation. We introduce the concept of regular tame exact Landau-Ginzburg system on a noncompact Kaehler…

In this note we give a new existence proof for the universal extension classes for $GL_2$ previously constructed by Friedlander and Suslin via the theory of strict polynomial functors. The key tool in our approach is a calculation of Parker…

In this article, we prove a $p$-adic analogue of the local invariant cycle theorem for $H^2$ in mixed characteristics. As a result, for a smooth projective variety $X$ over a $p$-adic local field $K$ with a proper flat regular model…

The holomorph of a discrete group $G$ is the universal semi-direct product of $G$. In chapter 1 we describe why it is an interesting object and state main results. In chapter 2 we recall the classical definition of the holomorph as well as…

Any abstract (not necessarily continuous) group automorphism of a simple, compact Lie group must be continuous due to Cartan (1930) and van der Waerden (1933). The purpose of this paper is to study a similar question in nilpotent Lie…

Following earlier work with Cris Negron on the cohomology of Drinfeld doubles $D(\mathbb G_{(r)})$, we develop a "geometric theory" of support varieties for "extended Drinfeld doubles" $\tilde D(\mathbb G_{(r)})$ of Frobenius kernels…

Each finite $p$-perfect group $G$ ($p$ a prime) has a universal central $p$-extension. For a perfect group these central extensions come from its {\sl Schur multiplier}. Serre gave a Stiefel-Whitney class approach to analyzing spin covers…

We show that the Nakayama automorphism of a Frobenius algebra $R$ over a field $k$ is independent of the field (Theorem 4). Consequently, the $k$-dual functor on left $R$-modules and the bimodule isomorphism type of the $k$-dual of $R$, and…

C*-endomorphisms arising from superselection structures with non-trivial centre define a 'rank' and a 'first Chern class'. Crossed products by such endomorphisms involve the Cuntz-Pimsner algebra of a vector bundle having the…

The Kr\"otz-Stanton Extension Theorem states that the orbit map of a K-finite vector in a Hilbert representation of a linear Lie group extends to a holomorphic map to a principal fibre bundle over the complex crown domain associated to the…

It is shown that the multiplicative monoids of Temperley-Lieb algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a self-adjunction is found in a…

We show that every group $G$ embeds malnormally into a simple, complete co-Hopfian group $H$. This implies that a non-trivial endomorphism of $G$ extends to $H$ if and only if it is an inner automorphism, strengthening a theorem of Schupp…

We establish theorems on the existence and compactness of solutions to the $\sigma_2$-Nirenberg problem on the standard sphere $\mathbb S^2$. A first significant ingredient, a Liouville type theorem for the associated fully nonlinear…

We study a saturated fusion system F on a finite 2-group S having a Baumann component based on a dihedral 2-group. Assuming F is 2-perfect with no nontrivial normal 2-subgroups, and the centralizer of the component is a cyclic 2-group, it…