Related papers: A type III$_1$ factor with the smallest outer auto…

We classify all decompositions of $M_3(\mathbb{C})$ into a direct vector-space sum of two subalgebras such that one of the subalgebras contains the identity matrix.

We prove that, for any positive integer $c$, the quotient group $\gamma_{c}(M_{3})/\gamma_{c+1}(M_{3})$ of the lower central series of the McCool group $M_{3}$ is isomorphic to two copies of the quotient group…

We explore the possibilities for elementary embeddings $j : M \to N$, where $M$ and $N$ are models of ZFC with the same ordinals, $M \subseteq N$, and $N$ has access to large pieces of $j$. We construct commuting systems of such maps…

We construct a compact closed category out of any symmetric monoidal category by freely adding adjoints to its objects. The morphisms of the completion are defined as string diagrams annotated by objects and morphisms from the original…

We establish the following non-abelian analogue of the Fundamental Theorem of Projective Geometry: the natural map from ${\rm{Aut}}(F_n)$ to the automorphism group of the free-factor complex $\mathcal{AF}_n$ is an isomorphism. We also prove…

It is known that the automorphism group of any projective K3 surface is finitely generated [24]. In this paper, we consider a certain kind of K3 surfaces with Picard number 3 whose automorphism groups are isomorphic to congruence subgroups…

In this paper we study \emph{threefolds isogenous to a product of mixed type} i.e. quotients of a product of three compact Riemann surfaces $C_i$ of genus at least two by the action of a finite group $G$, which is free, but not diagonal. In…

Let $G=G_1 \ast \ldots \ast G_k \ast F_N$ be a free product of finitely presented groups, where $F_N$ is a free group of rank $N \in \mathbb{N}$. Let $\mathrm{Out}(G,\mathcal{G})$ be the subgroup of $\mathrm{Out}(G)$ preserving the set of…

A smooth cuboid can be identified with a $3\times 3$ matrix of linear forms, with coefficients in a field $K$, whose determinant describes a smooth cubic in the projective plane. To each such matrix one can associate a group scheme over…

We prove that if a separable II$_1$ factor $M$ is existentially closed, then every $M$-bimodule is weakly contained in the trivial $M$-bimodule, $\text{L}^2(M)$, and, equivalently, every normal completely positive map on $M$ is a pointwise…

Let R be a commutative noetherian ring. We give criteria for a complex of cotorsion flat R-modules to be minimal, in the sense that every self homotopy equivalence is an isomorphism. To do this, we exploit Enochs' description of the…

Suppose that $f\colon X\to\mathrm{Spec}\, R$ is a minimal model of a complete local Gorenstein 3-fold, where the fibres of $f$ are at most one dimensional, so by [VdB1d] there is a noncommutative ring $\Lambda$ derived equivalent to $X$.…

A rigid automorphism of a linking system is an automorphism which restricts to the identity on the Sylow subgroup. A rigid inner automorphism is conjugation by an element in the center of the Sylow subgroup. At odd primes, it is known that…

Given a free product $G$, we investigate the existence of faithful free representations of the outer automorphism group $\text{Out}(G)$, or in other words of embeddings of $\text{Out}(G)$ into $\text{Out}\left(F_m\right)$ for some $m$. This…

We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…

Let (S, B) be the log pair associated with a projective completion of a smooth quasi-projective surface V . Under the assumption that the boundary B is irreducible, we obtain an algorithm to factorize any automorphism of V into a sequence…

Our main result is the following: let X be a normal affine toric surface without torus factor. Then there exists a non-normal affine toric surface X' with automorphism group isomorphic to the automorphism group of X if and only if X is…

For any abstract subfactor planar algebra $P$, there exists a finite index extremal subfactor $M_0 \subset M_1$ with $P$ as its standard invariant. In this paper, we classify the automorphism group of a bipartite graph planar algebra, and…

We provide a uniform framework to study the exceptional homogeneous compact geometries of type C3. This framework is then used to show that these are simply connected, answering a question by Kramer and Lytchak, and to calculate the full…

It has been proven by Schupp and Bergman that the inner automorphisms of groups can be characterized purely categorically as those group automorphisms that can be coherently extended along any outgoing homomorphism. One is thus motivated to…