Related papers: Maximal abelian subgroups of compact simple Lie gr…
For every field $F$ which has a quadratic extension $E$ we show there are non-metabelian infinite-dimensional thin graded Lie algebras all of whose homogeneous components, except the second one, have dimension $2$. We construct such Lie…
We extend the classification of solvable Lie algebras with abelian nilradicals to classify solvable Leibniz algebras which are one dimensional extensions of an abelian nilradicals.
We classify all real three dimensional Lie bialgebras. In each case, their automorphism group as Lie bialgebras is also given.
All gradings by abelian groups are classified on the following algebras over an algebraically closed field of characteristic not 2: the simple Lie algebra of type $G_2$ (characteristic not 3), the exceptional simple Jordan algebra, and the…
In this paper, we will show that nonabelian simple classical groups of Lie type are uniquely determined by the structure of their complex group algebras.
We classify group gradings on the simple Lie algebras of types $G_2$ and $D_4$ over the field of real numbers (or any real closed field): fine gradings up to equivalence and $G$-gradings, with a fixed group $G$, up to isomorphism.
We classify the solvable subalgebras, semisimple subalgebras, and Levi decomposable subalgebras of $\mathfrak{so}(4,\mathbb{C})$, up to inner automorphism. By Levi's Theorem, this is a full classification of the subalgebras of…
In this paper, we develop a new method to classify abelian automorphism groups of hypersurfaces. We use this method to classify (Theorem 4.2) abelian groups that admit a liftable action on a smooth cubic fourfold. A parallel result (Theorem…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
We carry out the Cantor-Bendixson analysis of the space of all subgroups of any countable abelian group and we deduce a complete classification of such spaces up to homeomorphism.
In this paper, we classify the finite simple groups with an abelian Sylow subgroup.
We classify abelian subgroups of Out(F_n) up to finite index in an algorithmic and computationally friendly way. A process called disintegration is used to canonically decompose a single rotationless element \phi into a composition of…
We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.
We prove that the automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields are cyclic, and give a complete list of finite groups that can be realized as such automorphism groups.
We determine the maximal dimension of compact subvarieties of $\mathcal{A}_g$, the moduli space of complex principally polarized abelian varieties of dimension $g$, and the maximal dimension of a compact subvariety through a very general…
Let $X$ be a complex projective variety. Suppose that the group of birational automorphisms of $X$ contains finite subgroups isomorphic to $(\mathbb{Z}/N\mathbb{Z})^r$ for $r$ fixed and $N$ arbitrarily large. We show that $r$ does not…
In this paper we classify all Riemann surfaces having a large abelian group of automorphisms, that is having an abelian group of automorphism of order strictly bigger then $4(g-1)$, where $g$ denotes as usual the genus of the Riemann…
We give a new computer-assisted proof of the classification of maximal subgroups of the simple group ${}^2E_6(2)$ and its extensions by any subgroup of the outer automorphism group $S_3$. This is not a new result, but no earlier proof…
By the algebraization of affine Nash groups, a connected affine Nash group is an abelian Nash manifold if and only if its algebraization is a real abelian variety. We first classify real abelian varieties up to isomorphisms. Then with a bit…
We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These sixteen Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical…