Related papers: Solvability of commutative automorphic loops

Among (isotopy classes of) automorphisms of handlebodies those called irreducible (or generic) are the most interesting, analogues of pseudo-Anosov automorphisms of surfaces. We consider the problem of isotoping an irreducible automorphism…

We introduce a recursive method to deconstruct the automorphism group of an ordered set. By connecting this method with deep results for permutation groups, we prove the Automorphism Conjecture for ordered sets of width less than or equal…

We show that the Skolem Problem is decidable in finitely generated commutative rings of positive characteristic. More precisely, we show that there exists an algorithm which, given a finite presentation of a (unitary) commutative ring…

We prove that if the Lyapunov spectrum of the Kontsevich-Zorich cocycle over an affine SL$(2,\mathbb{R})$-invariant submanifold is completely degenerate, i.e. $\lambda_2 = \cdots = \lambda_g = 0$, then the submanifold must be an arithmetic…

The singularity structure of solutions of a class of Hamiltonian systems of ordinary differential equations in two dependent variables is studied. It is shown that for any solution, all movable singularities, obtained by analytic…

We prove a new automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call `potential diagonalizability'. This result allows for `change of weight' and seems to be substantially more flexible…

Two unanswered questions in the heart of the theory of Leavitt path algebras are whether Grothendieck group $K_0$ is a complete invariant for the class of unital purely infinite simple algebras and, a weaker question, whether $L_2$ (the…

We consider applications of a finitary version of the Affine Representability theorem, which follows from recent work of Belov-Kanel, Rowen, and Vishne. Using this result we are able to show that when given a finite set of polynomial…

We determine the structure of automorphism group or each nonsplit metacyclic 2-group. This completes the work on automorphism groups of metacyclic $p$-groups.

We give a sharp bound for the automorphism group of a cubic simple graph with a given number of vertices. For each number of vertices we give an explicit graph attaining the bound, and prove its uniqueness in special cases.

Let $T$ be a locally finite tree all of whose vertices have valency at least $6$. We classify, up to isomorphism, the closed subgroups of $\mathrm{Aut}(T)$ acting $2$-transitively on the set of ends of $T$ and whose local action at each…

This is a survey paper presenting the history and both old and new results related to Kostant's problem. This problem asks for which modules over a semi-simple finite dimensional complex Lie algebra, the universal enveloping algebra…

We proved that any Lorentz transformation of 2-torus is Anosov automorphism. One completely describes admissible parameters of Lorentz transformations and their arithmetical properties. One proved that an admissible speed light parameter…

We classify all uniserial modules of the solvable Lie algebra $\mathfrak{g}=\langle x\rangle \ltimes V$, where $V$ is an abelian Lie algebra over an algebraically closed field of characteristic 0 and $x$ is an arbitrary automorphism of $V$.

We prove that it is decidable if a finitely based permutation class contains infinitely many simple permutations, and establish an unavoidable substructure result for simple permutations: every sufficiently long simple permutation contains…

A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to…

Let A be a separable unital nuclear purely infinite simple C*-algebra satisfying the Universal Coefficient Theorem, and such that the K_0-class of the identity is zero. We prove that every automorphism of order two of the K-theory of A is…

$2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed curves where several sheets meet. We show that the word problem for fundamental groups of $2$-stratifolds is solvable.

In this paper, we introduce a notion of unistructural cluster algebras, for which the set of cluster variables uniquely determines the clusters. We prove that cluster algebras of Dynkin type and cluster algebras of rank 2 are unistructural,…

A cluster automorphism is a $\mathbb{Z}$-algebra automorphism of a cluster algebra $\mathcal A$ satisfying that it sends a cluster to another and commutes with mutations. Chang and Schiffler conjectured that a cluster automorphism of…