Composition of Lie Group Elements from Basis Lie Algebra Elements
نویسندگان
چکیده
منابع مشابه
A differential equation for diagonalizing complex semisimple Lie algebra elements
In this paper, we consider a generalization of Ebenbauer’s differential equation for non-symmetric matrix diagonalization to a flow on arbitrary complex semisimple Lie algebras. The flow is designed in such a way that the desired diagonalizations are precisely the equilibrium points in a given Cartan subalgebra. We characterize the set of all equilibria and establish a Morse-Bott type property ...
متن کاملUniversity of Cambridge Approximating the Exponential from a Lie Algebra to a Lie Group Approximating the Exponential from a Lie Algebra to a Lie Group
Consider a diierential equation y 0 = A(t; y)y; y(0) = y0 with y0 2 G and A : R + G ! g, where g is a Lie algebra of the matricial Lie group G. Every B 2 g can be mapped to G by the matrix exponential map exp (tB) with t 2 R. Most numerical methods for solving ordinary diierential equations (ODEs) on Lie groups are based on the idea of representing the approximation yn of the exact solution y(t...
متن کاملLie Elements and Knuth Relations
A coplactic class in the symmetric group Sn consists of all permutations in Sn with a given Schensted Q-symbol, and may be described in terms of local relations introduced by Knuth. Any Lie element in the group algebra of Sn which is constant on coplactic classes is already constant on descent classes. As a consequence, the intersection of the Lie convolution algebra introduced by Patras and Re...
متن کاملLattice of full soft Lie algebra
In this paper, we study the relation between the soft sets and soft Lie algebras with the lattice theory. We introduce the concepts of the lattice of soft sets, full soft sets and soft Lie algebras and next, we verify some properties of them. We prove that the lattice of the soft sets on a fixed parameter set is isomorphic to the power set of a ...
متن کاملWhat Does a Lie Algebra Know about a Lie Group?
We define Lie groups and Lie algebras and show how invariant vector fields on a Lie group form a Lie algebra. We prove that this correspondence respects natural maps and discuss conditions under which it is a bijection. Finally, we introduce the exponential map and use it to write the Lie group operation as a function on its Lie algebra.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 2021
ISSN: 1776-0852
DOI: 10.1080/14029251.2018.1503398