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We classify the automorphisms of the (chiral) level-k affine SU(3) fusion rules, for any value of k, by looking for all permutations that commute with the modular matrices S and T. This can be done by using the arithmetic of the cyclotomic…

An example of a non-triangulable locally nilpotent derivation and an example of a wild exponential automorphism of the free Novikov algebra $N\left\langle x,y,z\right\rangle$ in three variables $x,y,z$ over a field of characteristic zero…

The semigroup of the homotopy classes of the self-homotopy maps of a finite complex which induce the trivial homomorphism on homotopy groups is nilpotent. We determine the nilpotency of these semigroups of compact Lie groups and finite Hopf…

An automorphism on a complex supermanifold $\mathcal M$ is called unipotent if it reduces to the identity on the associated graded supermanifold $gr(\mathcal M)$. These automorphisms are close to be complementary to those responsible for…

Let $G$ be a finite group minimally generated by $d(G)$ elements and $\Aut_c(G)$ denote the group of all (conjugacy) class-preserving automorphisms of $G$. Continuing our work [Class preserving automorphisms of finite $p$-groups, J. London…

For automorphisms of a polynomial ring in two variables over a domain R, we show that local tameness implies global tameness provided that every 2-generated invertible R-module is free. We give many examples illustrating this property.

In this paper we prove that every automorphism of a Chevalley group with the root system G_2 over a commutative ring R with 1/3, generated by all its invertible elements and the ideal 2R is a composition of ring and inner automorphisms.

We study the automorphism group of an infinite minimal shift $(X,\sigma)$ such that the complexity difference function, $p(n+1)-p(n)$, is bounded. We give some new bounds on $\mbox{Aut}(X,\sigma)/\langle \sigma \rangle$ and also study the…

In this article we continue the study of automorphism groups of constant length substitution shifts and also their topological factors. We show that up to conjugacy, all roots of the identity map are letter exchanging maps, and all other…

A combing is a set of normal forms for a finitely generated group. This article investigates the language-theoretic and geometric properties of combings for nilpotent and polycyclic groups. It is shown that a finitely generated class 2…

Let $K[x,y]$ be the polynomial algebra in two variables over an algebraically closed field $K$. We generalize to the case of any characteristic the result of Furter that over a field of characteristic zero the set of automorphisms $(f,g)$…

In this paper we prove that over algebraically closed field $K$ of positive characteristic $\neq 2$ every automorphism of the group of origin-preserving automorphisms of the polynomial algebra $K[x_1,\ldots, x_n]$ ($n>3$) which fixes every…

We construct an analogue of the Nagata automorphism of free nonassociative algebras and free commutative algebras of rank two over a Euclidean domain and prove that it is wild.

A permutation of the point set of the affine space $AG(n,q)$ is called an integral automorphism if it preserves the integral distance defined among the points. In this paper, we complete the classification of the integral automorphisms of…

We find all possible isomorphisms and 3-birational maps (i.e., birational maps which induce an isomorphism between open subsets whose respective complements have codimension at least 3) between moduli spaces of parabolic vector bundles with…

The action of ring automorphisms of the polynomial ring in two variables over the real numbers on real plane curves is considered. The orbits containing degree-three polynomials are computed, with one representative per orbit being…

There is a one-to-one correspondence between involutory latin quandles and uniquely $2$-divisible Bruck loops. Bruck loops of odd prime power order are centrally nilpotent. Using linear-algebraic approach to central extensions, we enumerate…

Let X be an affine irreducible variety over an algebraically closed field k of characteristic zero. Given an automorphism F, we denote by k(X)^F its field of invariants, i.e. the set of rational functions f on X such that f(F)=f. Let n(F)…

This article initiates a geometric study of the automorphism groups of general graph products of groups, and investigates the algebraic and geometric structure of automorphism groups of cyclic product of groups. For a cyclic product of at…

Let $G$ be a finite group and $H$ a subgroup of $G$. Each left transversal (with identity) of $H$ in $G$ has a left loop (left quasigroup with identity) structure induced by the binary operation of $G$. We say two left transversals are…