Related papers: Linear Representation of Lie Group
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
We discuss the possibility of very regular subgroups of a Lie group, in presence of an index figure. Further, representations that reduce action to a very regular boundary.
The main aim of this paper is to determine the multiplicative lie algebra structures on the semi-direct product of an abelian group with a group under certain conditions.
In Part I of this series we presented the general ideas of applying group-algebraic methods for describing quantum systems. The treatment was there very "ascetic" in that only the structure of a locally compact topological group was used.…
Second-order equations of motion on a group manifold that appear in a large class of so-called chiral theories are presented. These equations are presented and explicitely solved for cases of semi-simple, finite-dimensional Lie groups. With…
This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in…
We provide a motivated introduction to the theory of categorical actions of groups and the local geometric Langlands program. Along the way we emphasize applications, old and new, to the usual representation theory of reductive and affine…
These are lecture notes of a course on symmetry group analysis of differential equations, based mainly on P. J. Olver's book 'Applications of Lie Groups to Differential Equations'. The course starts out with an introduction to the theory of…
Any sufficiently often differentiable curve in the orbit space of a compact Lie group representation can be lifted to a once differentiable curve into the representation space.
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an…
These are notes of a graduate course on representations of non-compact semisimple Lie groups given by the author at MIT.
Using the Lie derivative of the metric we define a class of Lie algebras of vector fields by generalising the concept of Killing vectors. As a Lie algebra they define locally a group action on the pseudo-Riemannian manifold through…
A catalogue of explicit realizations of representations of (super) Lie algebras and quantum algebras in Fock space is presented.
We show that induced representations for a pair of $\textit{diffeological Lie groups}$ exist, in the form of an indexed colimit in the category of diffeological spaces.
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
We establish a few simple results on contragredient representations of Lie groups, with a view toward applications to the abstract characterization of some spaces of pseudo-differential operators. In particular, this method provides an…
We use the notion of the principal three-dimensional subgroup of a simple Lie group to identify certain special subspaces of the Lie algebra and address the question of whether these are calibrated for invariant forms on the group.
We provide detailed calculations for the classification of representations of compact simple Lie groups with non-empty boundary in the orbit space, first announced in a previous paper [arXiv:2112.00513] by the same authors.
Necessary and sufficient conditions for the exponentiation of finite-dimensional real Lie algebras of linear operators on complete Hausdorff locally convex spaces are obtained, focused on the equicontinuous case - in particular, necessary…
Theory of differential operators on associative algebras is not extended to the non-associative ones in a straightforward way. We consider differential operators on Lie algebras. A key point is that multiplication in a Lie algebra is its…