Related papers: Lie groups, algebraic groups and lattices
The aim of this paper is to present aspects of the use of Lie groups in mechanics. We start with the motion of the rigid body for which the main concepts are extracted. In a second part, we extend the theory for an arbitrary Lie group and…
In present work, we find a class of Lie algebras, which are defined from the symmetrizable generalized intersection matrices. However, such algebras are different from generalized intersection matrix algebras and intersection matrix…
We show Lie algebra versions of some results on homological finiteness properties of subdirect products of groups, including a version of the 1-2-3 Theorem.
Necessary or sufficient conditions are presented for the existence of various types of actions of Lie groups and Lie algebras on manifolds.
This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…
It is shown that there is a $C^*$-algebraic quantum group related to any double Lie group. An algebra underlying this quantum group is an algebra of a differential groupoid naturally associated with a double Lie group
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…
In this paper we define a new algebraic object: the disguised-groups. We show the main properties of the disguised-groups and, as a consequence, we will see that disguised-groups coincide with regular semigroups. We prove many of the…
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…
This is the note for the four lectures given by the author in the ``International Short-School/Conference on Affine Algebraic Geometry and the Jacobian Conjecture" at Chern Institute of Mathematics, Nankai University, Tianjin, China. July…
Following Robert's [26], we study the structure of unitary groups and groups of approximately inner automorphisms of unital $C^*$-algebras, taking advantage of the former being Banach-Lie groups. For a given unital $C^*$-algebra $A$, we…
An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.
We study the lower central series of a right-angled Coxeter group $RC_K$ and the associated Lie algebra $L(RC_K)$. The latter is related to the graph Lie algebra $L_K$. We give an explicit combinatorial description of the first three…
We introduce a generalization of Lie algebras within the theory of nonhomogeneous quadratic algebras and point out its relevance in the theory of quantum groups. In particular the relation between the differential calculus on quantum group…
We determine many of the atoms of the algebraic lattices arising in $\mathfrak{q}$-theory of finite semigroups.
These are expanded lecture notes from the author's minicourse at the 2022 Poisson Geometry Summer School, which took place at the Centre de Recerca Matematica in Barcelona, Spain. After giving a general introduction to wonderful varieties,…
This is an overview article on compact Lie groups and their representations, written for the Encyclopedia of Mathematical Physics to be published by Elsevier.
While describing the results of our recent work on exceptional Lie and Jordan algebras, so tightly intertwined in their connection with elementary particles, we will try to stimulate a critical discussion on the nature of spacetime and…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
A frame-independent formulation of Lie brackets on affine spaces or {\em Lie affebras} introduced in [K.\ Grabowska, J.\ Grabowski \& P.\ Urba\'nski, Lie brackets on affine bundles, {\em Ann.\ Global Anal.\ Geom.} {\bf 24} (2003), 101--130]…