Related papers: Automorphisms and isomorphisms of Chevalley groups…

In this paper we prove that every automorphism of (elementary) adjoint Chevalley group with root system of rank $>1$ over a commutative ring (with 1/2 for the systems $A_2$, $F_4$, $B_l$, $C_l$; with 1/2 and 1/3 for the system $G_2$) is…

In this paper we prove that every automorphism of a Chevalley group (or its elementary subgroup) with root system of rank >1 over a commutative ring (with 1/2 for the systems A_2, F_4, B_l, C_l; with 1/2 and 1/3 for the system G_2) is…

In the paper we prove that every automorphism of and elementary adjoint Chevalley group of types $A_l, D_l$, or $E_l$, over local commutative ring with 1/2 is a composition of a ring automorphism and conjugation by some matrix from the…

In the paper we prove that every automorphism of any adjoint Chevalley group of types B_2 or G_2 is standard, i.e., it is a composition of the ``inner'' automorphism, ring automorphism and central automorphism.

We construct certain integral structures for the cores of reduced tame extended affine Lie algebras of rank at least 2. One of the main tools to achieve this is a generalization of Chevalley automorphisms in the context of extended affine…

We prove that every isomorphism of Chevalley groups of type $G_2$ over commutative local rings with 1/2 and 1/3 is standard, i. e., it is a composition of a ring isomorphism and an inner automorphism.

In the paper we prove that every automorphism of a (elementary) Chevalley group of type $A_l, D_l$, or $E_l$, $l\geqslant 2$, over a commutative local ring with 1/2 is standard, i. e., is the composition of inner, ring, graph and central…

In the paper we prove that every automorphism of a Chevalley group of type $F_4$ over a commutative local ring with~1/2 is standard, i. e., it is a composition of ring and inner automorphisms.

A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.

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 describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…

We study automorphism groups of formal matrix algebras. We also consider automorphisms of ordinary matrix algebras (in particular, triangular matrix algebras).

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

The paper presents the complete classification of Automorphic Lie Algebras based on $\mathfrak{sl}_n (\mathbb{C})$, where the symmetry group $G$ is finite and the orbit is any of the exceptional $G$-orbits in $\overline{\mathbb{C}}$. A key…

We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…

In the given paper we prove that every automorphism of a Chevalley group of type $B_l$, $l\geqslant 2$, over a commutative local ring with 1/2 is standard, i. e., it is a composition of ring, inner and central automorphisms.

In this paper, we continue our study of abstract representations of elementary subgroups of Chevalley groups of rank $\geq 2.$ First, we extend our earlier methods to analyze representations of elementary groups over arbitrary associative…

We classify abelian subgroups of the automorphism group of any compact simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup. This leads to a classification of the maximal abelian subgroups of compact…

The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.

The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.