Related papers: Levi decomposition of nilpotent centralisers in cl…
New systems of Laplace (Casimir) operators for the orthogonal and symplectic Lie algebras are constructed. The operators are expressed in terms of paths in graphs related to matrices formed by the generators of these Lie algebras with the…
The present article studies nilpotent and Hamiltonian cancellative residuated lattices and their relationship with nilpotent and Hamiltonian lattice-ordered groups. In particular, results about lattice-ordered groups are extended to the…
It is known that the set of irreducible components of nilpotent varieties provides a geometric realization of the crystal basis for quantum groups. For each reduced expression of a Weyl group element, Gei{\ss}, Leclerc and Schr\"{o}er has…
Let F be an algebraically closed field and let G be a semisimple F-algebraic group for which the characteristic of F is *very good*. If X in Lie(G) = Lie(G)(F) is a nilpotent element in the Lie algebra of G, and if C is the centralizer in G…
We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic image of a finite group…
We investigate symplectic nilpotent Lie groups with Lagrangian normal subgroups. We show that there exists a bijection between the isomorphism classes of nilpotent Lie groups with Lagrangian normal subgroups and the isomorphism classes of…
We adapt the abstract concepts of abelianness and centrality of universal algebra to the context of inverse semigroups. We characterize abelian and central congruences in terms of the corresponding congruence pairs. We relate centrality to…
We give a unified description of twisted forms of classical reductive groups schemes. Such group schemes are constructed from algebraic objects of finite rank, excluding some exceptions of small rank. These objects, augmented odd form…
We study left invariant contact forms and left invariant symplectic forms on Lie groups. We give the classification of all symplectic structures on nilpotent Lie algebras up the dimension 6.
In this paper subcentral (resp., central) idempotent series and composition subcentral (resp., central) idempotent series in an inverse semigroup are introduced and investigated. It is shown that if $S=EG$ is a factorizable inverse monoids…
Like the lower central series of a nilpotent group, filters generalize the connection between nilpotent groups and graded Lie rings. However, unlike the case with the lower central series, the associated graded Lie ring may share few…
The connections between Euler's equations on central extensions of Lie algebras and Euler's equations on the original, extended algebras are described. A special infinite sequence of central extensions of nilpotent Lie algebras constructed…
This is the first of a series of papers devoted to certain pairs of commuting nilpotent elements in a semisimple Lie algebra that enjoy quite remarkable properties and which are expected to play a major role in Representation theory. The…
In studying nilpotent groups, the lower central series and other variations can be used to construct an associated $\mathbb{Z}^+$-graded Lie ring, which is a powerful method to inspect a group. Indeed, the process can be generalized…
In this paper we study gradings on simple Lie algebras arising from nilpotent elements. Specifically, we investigate abelian subalgebras which are degree 1 homogeneous with respect to these gradings. We show that for each odd nilpotent…
We give a uniform description of the decomposition of the unipotent variety of a classical group in arbitrary characteristic into pieces (considered in a non-uniform way in the earlier parts of this paper).
In this paper we discuss some of Springer's work on unipotent elements in a reductive groups and on representations of Weyl groups. Among the topics considered are Springer's bijection from the unipotent variety to the nilpotent variety,…
The structure of a solvable Lie groups admitting an Einstein left-invariant metric is, in a sense, completely determined by the nilradical of its Lie algebra. We give an easy-to-check necessary and sufficient condition for a nilpotent…
For a natural number $m$, a Lie algebra $L$ over a field $k$ is said to be of breadth type $(0, m)$ if the co-dimension of the centralizer of every non-central element is of dimension $m$. In this article, we classify finite dimensional…
This paper deals with naturally reductive pseudo-Riemannian 2-step nilpotent Lie groups $(N, \la \,,\,\ra_N)$, such that $\la \,,\,\ra_N$ is invariant under a left action. The case of nondegenerate center is completely characterized. In…