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On the Automorphism Group of a Lie Group [PDF]

Proceedings of the American Mathematical Society, 1974
It is proved that the automorphism group of a connected real or complex Lie group contains an open real or complex algebraic subgroup. It follows that the identity component of the group of complex automorphisms of a connected complex Lie group is a complex algebraic group.
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Jacobi–Lie symmetry and Jacobi–Lie T-dual sigma models on group manifolds

Nuclear Physics B, 2018
Using the concept of Jacobi–Lie group and Jacobi–Lie bialgebra, we generalize the definition of Poisson–Lie symmetry to Jacobi–Lie symmetry. In this regard, we generalize the concept of Poisson–Lie T-duality to Jacobi–Lie T-duality and present Jacobi–Lie
A. Rezaei-Aghdam, M. Sephid
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Einstein warped product spaces on Lie groups

Cubo, 2022
We consider a compact Lie group with bi-invariant metric, coming from the Killing form. In this paper, we study Einstein warped product space, $M = M_1 \times_{f_1} M_2$ for the cases, $(i)$ $M_1$ is a Lie group $(ii)$ $M_2$ is a Lie group and $(iii ...
Buddhadev Pal, Santosh Kumar, Pankaj Kumar   +2 more
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Regularity of Lie groups

Communications in Analysis and Geometry, 2022
72 pages.
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The Affine Group of a Lie Group [PDF]

Proceedings of the American Mathematical Society, 1963
1. If G is a Lie group, then the group Aut(G) of all continuous automorphisms of G has a natural Lie group structure. This gives the semidirect product A(G) = G-Aut(G) the structure of a Lie group. When G is a vector group R", A(G) is the ordinary affine group A(re). Following L. Auslander [l ] we will refer to A(G) as the affine group of G, and regard
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Dirac Lie groups [PDF]

Asian Journal of Mathematics, 2014
46 ...
Li-Bland, David, Meinrenken, Eckhard
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Controllabilty and stability analysis on a group associated with Black-Scholes equation [PDF]

Archives of Control Sciences, 2020
In this paper we have studied the driftless control system on a Lie group which arises due to the invariance of Black-Scholes equation by conformal transformations.
Archana, Tiwari, Debanjana, Bhattacharyya, K.C., Pati   +2 more
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The Lie Group in Infinite Dimension

Abstract and Applied Analysis, 2011
A Lie group acting on finite-dimensional space is generated by its infinitesimal transformations and conversely, any Lie algebra of vector fields in finite dimension generates a Lie group (the first fundamental theorem).
V. Tryhuk, V. Chrastinová, O. Dlouhý
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Generalized Lorentzian Ricci solitons on 3-dimensional Lie groups associated to the Bott Connection [PDF]

AUT Journal of Mathematics and Computing
In this paper, we investigate which one of the non-isometric left-invariant Lorentz metrics $g$ on $3$-dimensional Lie groups satisfies the generalized Ricci soliton equation $a{\rm Ric}^B [g] + \dfrac{b}{2}{\cal L}_{ X}^B g +cX^\flat\otimes X^\flat ...
Ghodratallah Fasihi Ramandi, Shahroud Azami, Vahid Pirhadi   +2 more
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Model Formulation Over Lie Groups and Numerical Methods to Simulate the Motion of Gyrostats and Quadrotors

Mathematics, 2019
The present paper recalls a formulation of non-conservative system dynamics through the Lagrange−d’Alembert principle expressed through a generalized Euler−Poincaré form of the system equation on a Lie group.
Simone Fiori
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