相关论文: Semisimple Algebraic Groups in Characteristic Zero

We show that finite-dimensional Lie algebras over a field of characteristic zero such that the second cohomology group in every finite-dimensional module vanishes, are, essentially, semisimple.

This paper contains a complete proof of a fundamental theorem on the normalizers of unipotent subgroups in semisimple algebraic groups.

We consider semisimple super Tannakian categories generated by an object whose symmetric or alternating tensor square is simple up to trivial summands. Using representation theory, we provide a criterion to identify the corresponding…

A theory of cyclic elements in semisimple Lie algebras is developed. It is applied to an explicit construction of regular elements in Weyl groups.

Given a connected linear algebraic group $G$, we descrive the subgroup of $G$ generated by all semisimple elements.

We continue studying properties of semisimple Hopf algebras $H$ over algebraically closed fields of characteristic 0 resulting from their generalized character tables. We show that the generalized character table of $H$ reflect normal left…

Characteristic Lie algebras of semi-discrete chains are studied. The attempt to adopt this notion to the classification of Darboux integrable chains has been undertaken.

In this article, we study the elements with disconnected centralizer in the Brauer complex associated to a simple algebraic group G defined over a finite field with corresponding Frobenius map F and derive the number of F-stable semisimple…

A classification of semisimple algebras of vector fields on C^N that have a Cartan subalgebra of dimension N is given. The proof uses basic representation theory and the local canonical form of semisimple Lie algebras of vector fields.

Let $G$ be a finite group. There is a standard theorem on the classification of $G$-equivariant finite dimensional simple commutative, associative, and Lie algebras (i.e., simple algebras of these types in the category of representations of…

We investigate the theory of affine group schemes over a symmetric tensor category, with particular attention to the tangent space at the identity. We show that this carries the structure of a restricted Lie algebra, and can be viewed as…

A Lie superalgebra is attached to any finite-dimensional J-ternary algebra over an algebraically closed field of characteristic 3, using a process of semisimplification via tensor categories. Some of the exceptional simple Lie algebras,…

A classification of the semisimple subalgebras of the Lie algebra of traceless $3\times 3$ matrices with complex entries, denoted $A_2$, is well-known. We classify its nonsemisimple subalgebras, thus completing the classification of the…

We determine the blocks of the walled Brauer algebra in characteristic zero. These can be described in terms of orbits of the action of a Weyl group of type $A$ on a certain set of weights. In positive characteristic we give a linkage…

It is shown that any finite dimensional simple Lie superalgebra over an algebraically closed field of characteristic 0 is generated by 2 elements.

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 observe that on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of characteristic $p> h$ (where $h$ is the Coxeter number), with a given (generalized) central character are…

We classify semisimple module categories over the tensor category of representations of quantum SL(2) extending previous results to the roots of unity and positive characteristic cases.

We prove that a finite-dimensional irreducible Hopf algebra $H$ in positive characteristic is semisimple, if and only if it is commutative and semisimple, if and only if the restricted Lie algebra $P(H)$ of the primitives is a torus. This…

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…