Related papers: Elementary abelian 2 subgroups of compact Lie grou…

Given a prime $p$, we construct a permutation group containing at least $p^{p-2}$ non-conjugated regular elementary abelian subgroups of order $p^3$. This gives the first example of a permutation group with exponentially many non-conjugated…

The Lie algbera of a compact semisimple Lie group G is determined by the degrees of the irreducible representations of G. However, two different groups can have the same representation degrees.

In this article we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebra of sections of the associated Lie…

We give a sharp bound for orders of elementary abelian 2-groups of birational automorphisms of rationally connected threefolds.

We extend results related to maximal subalgebras and ideals from Lie to Leibniz algebras. In particular, we classify minimal non-elementary Leibniz algebras and Leibniz algebras with a unique maximal ideal. In both cases, there are types of…

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…

We show that after mapping each element of a set of second class constraints to the surface of the other ones, half of them form a subset of abelian first class constraints. The explicit form of the map is obtained considering the most…

In this paper we present new formulas, which represent commutators and anticommutators of Clifford algebra elements as sums of elements of different ranks. Using these formulas we consider subalgebras of Lie algebras of pseudounitary…

We classify, up to isomorphism, the group gradings on the non-exceptional classical simple Lie superalgebras, except for type A(1,1), over an algebraically closed field of characteristic zero. To this end, we study graded-simple and…

Let S be a closed oriented surface of genus g > 1, and let T denote its Torelli group. First, given a set E of homotopically nontrivial, pairwise disjoint, pairwise nonisotopic simple closed curves on S, we determine precisely when a…

An adjoint Chevalley group of rank at least 2 over a rational algebra (or a similar ring), its elementary subgroup, and the corresponding Lie ring have the same automorphism group. These automorphisms are explicitly described.

The problem of enumeration of conjugacy classes of finite abelian subgroups of the mapping class group $\mathcal{M}_{\sigma}$ of a compact closed surface $X$ of genus $\sigma$ is considered. A complete method of enumeration is achieved for…

We provide characterizations of Lie groups as compact-like groups in which all closed zero-dimensional metric (compact) subgroups are discrete. The "compact-like" properties we consider include (local) compactness, (local)…

Algebraic structures such as monoids, groups, and categories can be formulated within a category using commutative diagrams. In many common categories these reduce to familiar cases. In particular, group objects in Grp are abelian groups,…

Let $p$ be an odd prime, and let $S$ be a $p$-group with a unique elementary abelian subgroup $A$ of index $p$. We classify the simple fusion systems over all such groups $S$ in which $A$ is essential. The resulting list, which depends on…

Working over an arbitrary field, we define compact semisimple 2-categories, and show that every compact semisimple 2-category is equivalent to the 2-category of separable module 1-categories over a finite semisimple tensor 1-category. Then,…

In this paper we give invariants that characterize isotypically equivalent Abelian periodic groups. Also, we describe types of standart tuples of elements in these groups. As the particular case we prove that two Abelian $p$-groups with…

The complete affine structures on abelian Lie algebras in small dimensions are well known. In this paper we are interested by the non complete case. In particular we classify all these structures in dimensions 2 and 3.

In this paper we classify the reducible representations of compact simple Lie groups all of whose orbits are tautly embedded in Euclidean space with respect to Z_2 coefficients.

Constructions of n-Lie algebras by strong n-Lie-Poisson algebras are given. First cohomology groups of adjoint module of Jacobian algebras are calculated. Minimal identities of 3-Jacobian algebra are found.