Lie group

(redirected from Transformation groups)

Lie group

[′lē ‚grüp]
(mathematics)
A topological group which is also a differentiable manifold in such a way that the group operations are themselves analytic functions.
References in periodicals archive ?
Personal Training/body transformation groups My personal training clients and six-week body transformation groups are accountable with their food every week and they have their body statistics taken every two weeks.
Miwa, "Transformation groups for soliton equations VI-KP hierarchies of orthogonal and symplectic type," Journal of the Physical Society of Japan, vol.
A basic problem in the theory of transformation groups is to find necessary and sufficient conditions for the existence of a G-equivariant map between two G-spaces.
The progress in this direction will shed new light on the structure of these transformation groups playing a fundamental role in geometry, topology and dynamics.
Introducing the work of mathematicians Lie (1842u99) and Klein (1849u1925), mathematicians and theoretical physicists focus on the Erlangen program that Klein wrote and Lie contributed to, and which provides a fundamental point of view on the place of transformation groups in mathematics and physics.
"We have seen a renewed focus on internal transformation groups. It's our hope that these groups don't get their attention subdivided into 15 different high-priority projects that all must be done right now," she says.
yields the overdetermined system of linear equations called the determining equation which may be solved to obtain the admitted symmetry generators (or equivalently symmetry transformation groups).
In the late eighteen century Sophus Lie made use of transformation groups in an effort to bring the results of Evarist Galois on polinomial equations to the differential equations theory.
He covers finite differences and transformation groups in space of discrete variables, invariance in finite-difference models, invariant difference models of ordinary differential equations and partial differential equations, combined mathematical models and some generalizations, Lagrangian formalism for difference equations, symmetries and first integrals and symmetries in Hamiltonian formalisms for difference equations, and the discrete representation of ordinary differential equations with symmetries.
Striving for balance between general theory and concrete examples, the book adopts a probabilistic perspective, stressing the invariance of considered point processes under natural transformation groups. Chapters cover Gaussian analytic functions (GAFs), joint intensities, determinantal point processes, the hyperbolic GAF, a determinantal zoo, and large deviations for zeros.
From the viewpoint of transformation groups, one noteworthy property is that [Sigma](2, 3, 5) is the only nonsimply connected homology sphere admitting a transitive action of a compact Lie group [Br1].
I have seen a huge rise in clients over-60 training in all our exercise sessions we offer including our Beach Bootcamps, Outdoor Gym strength sessions, Personal Training, indoor Bootcamps and our 6 week body transformation groups. In fact, due to the demand we also run specific small group sessions for the over-60s and there is certainly no let-up in intensity, as all sessions are designed so each individual can work as hard as they wish, at their own level.

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