相关论文: Simple finite group schemes and their infinitesima…

In this expository paper, we first review the classification of the restricted simple Lie algebras in characteristic different from 2 and 3 and then we describe their infinitesimal deformations. We conclude by indicating some possible…

We compute the restricted infinitesimal deformations of the restricted simple Lie algebras over an algebraically closed field of characteristic different from 2 and 3.

We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…

We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…

The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum, in particular, to list all finite simple groups for…

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically…

The notion of a Lie conformal superalgebra encodes an axiomatic descrption of singular parts of the operator product expansions of chiral fields in conformal field theory. In the paper we give a detailed proof of the classification of all…

We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative…

We prove that infinite definably simple locally finite groups of finite centraliser dimension are simple groups of Lie type over locally finite fields. Then, we identify conditions on automorphisms of a stable group that make it resemble…

We classify, up to equivalence, all finite-dimensional simple graded division algebras over the field of real numbers. The grading group is any finite abelian group.

For any finitely generated abelian group $Q$, we reduce the problem of classification of $Q$-graded simple Lie algebras over an algebraically closed field of "good" characteristic to the problem of classification of gradings on simple Lie…

The classification of gradings by abelian groups on finite direct sums of simple finite-dimensional nonassociative algebras over an algebraically closed field is reduced, by means of the use of loop algebras, to the corresponding problem…

We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.

We compute the infinitesimal deformations of two families of restricted simple Lie algebras: the contact and the Hamiltonian algebras.

A classification of (countable) direct limits of finite dimensional involution simple associative algebras over an algebraically closed field of arbitrary characteristic is obtained. This also classifies the corresponding dimension groups.…

All simple weight modules with finite dimensional weight spaces over affine Lie algebras are classified.

In this paper, we use (bi)semicosimplicial language to study the classical problem of infinitesimal deformations of a closed subscheme in a fixed smooth variety, defined over an algebraically closed field of characteristic 0. In particular,…

We determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the Wedderburn decompositions have the least number of simple components. We apply our work to obtain similar…

For those deformations that satisfy a certain non-degeneracy condition, we describe the structure of certain simple modules of the deformations of the subcharacter algebra of a finite group. For finite abelian groups, we prove that the…

In this report we summarize this work, all finite simple groups $G$ can determined uniformly using their orders $|G|$ and the set $\pi_e(G)$ of their element orders.