论有限维代数自同构群的可解性

The group of automorphisms of semigroup of endomorphisms of free commutative and free associative algebras

In this paper are described the groups of automorphisms of semigroup End(W(X)), where W(X) is free commutative or free associative algebra.

Automorphisms of cluster algebras of rank 2

We compute the automorphism group of the affine surfaces with the coordinate ring isomorphic to a cluster algebra of rank 2.

The inversion formula for automorphisms of the Weyl algebras and polynomial algebras

The inversion formula is given for automorphisms of the Weyl algebras with polynomial coefficients over a field of characteristic zero. The theorem of Gabber on the degree of polynomial automorphism is extended. It is proved that any automorphism of the Weyl algebra with polynomial coefficients is determined by its left (right) faces (extending the result of J. H. McKay and S. S.-S. Wang for polynomial automorphisms).

The group of automorphisms of the Jacobian algebra $\mA_n$

The groups of automorphisms of the Jacobian algebras are found.

The group of automorphisms of the Lie algebra of derivations of a polynomial algebra

We prove that the group of automorphisms of the Lie algebra $\Der_K (P_n)$ of derivations of a polynomial algebra $P_n=K[x_1,..., x_n]$ over a field of characteristic zero is canonically isomorphic to the the group of automorphisms of the polynomial algebra $P_n$.

The group of automorphisms of the algebra of one-sided inverses of a polynomial algebra, II

Explicit generators are found for the group of automorphisms of the algebra of one-sided inverses of a polynomial algebra in $n$ variables. An analogue of the polynomial Jacobian homomorphism is found.

The groups of automorphisms of the Lie algebras of unitriangular polynomial derivations

The groups of automorphisms of the Lie algebras of unitriangular polynomial derivations are found.

The groups of automorphisms of the Lie algebras of polynomial vector fields with zero or constant divergence

The group of automorphisms is found for the Lie algebra of polynomial vector fields with constant divergence.

The groups of automorphisms of the Lie algebras of formally analytic vector fields with constant divergence

The groups of automorphisms of the Lie algebras of formally analytic vector fields with constant divergence are found.

Every monomorphism of the Lie algebra of unitriangular polynomial derivations is an automorphism

We prove that every monomorphism of the Lie algebra $\ggu_n$ of unitriangular derivations of the polynomial algebra $P_n=K[x_1,..., x_n]$ is an automorphism.

On group automorphisms in universal algebraic geometry

In this paper, we study group equations with occurrences of automorphisms. We describe equational domains in this class of equations. Moreover, we solve a number of open problem posed in universal algebraic geometry.

The Anick automorphism of free associative algebras

We prove that the well-known Anick automorphism of the free associative algebra F<x,y,z> over an arbitrary field F of characteristic 0 is wild.

Automorphisms of the Weyl algebra

We discuss a conjecture which says that the automorphism group of the Weyl algebra in characteristic zero is canonically isomorphic to the automorphism group of the corresponding Poisson algebra of classical polynomial symbols. Several arguments in favor of this conjecture are presented, all based on the consideration of the reduction of the Weyl algebra to positive characteristic.

A software package to compute automorphisms of graded algebras

We present a library autgradalg.lib for the free computer algebra system Singular to compute automorphisms of integral, finitely generated $\mathbb{C}$-algebras that are graded pointedly by a finitely generated abelian group. It implements the algorithms developed in 'Computing automorphisms of Mori dream spaces'. We apply the algorithms to Mori dream spaces and investigate the automorphism groups of a series of Fano varieties.

有限生成顶点代数的自同构群的可表示性

Representability of the automorphism group of finitely generated vertex algebras

研究自由代数的自同构群，证明有限生成顶点代数在其noetherian环上的自同构群为仿射群方案。

有限维单项代数由其自同构群确定

Finite-dimensional monomial algebras are determined by their automorphism group

本文证明有限维单项代数在其自同构群下被唯一确定，展示了如何通过自同构群恢复单项理想。