User ’ S Guide to Semidirect Product Reduction Theory
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چکیده
Here we carry out computations that help clarify the La-grangian and Hamiltonian structure of compressible flow. The intent is to be pedagogical and rigorous, providing concrete examples of the the
منابع مشابه
Symplectic Reduction for Semidirect Products and Central Extensions
This paper proves a symplectic reduction by stages theorem in the context of geometric mechanics on symplectic manifolds with symmetry groups that are group extensions. We relate the work to the semidirect product reduction theory developed in the 1980’s by Marsden, Ratiu, Weinstein, Guillemin and Sternberg as well as some more recent results and we recall how semidirect product reduction finds...
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Within the usual semidirect product S ∗ T of regular semigroups S and T lies the set Reg (S ∗ T ) of its regular elements. Whenever S or T is completely simple, Reg (S ∗T ) is a (regular) subsemigroup. It is this ‘product’ that is the theme of the paper. It is best studied within the framework of existence (or e-) varieties of regular semigroups. Given two such classes, U and V, the e-variety U...
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In his 1996 work developing the theory of association schemes as a ‘generalized’ group theory, Zieschang introduced the concept of the semidirect product as a possible product operation of certain association schemes. In this paper we extend the semidirect product operation into the entire set of association schemes. We then derive a way to decompose certain association schemes into smaller ass...
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After precalculus, mathematics tudents often leave behind the familiar family of transformations, x Fax + b. We will show that this family, when examined in the right light, leads us to some interesting and important ideas in group theory. By building on this accessible example, it is possible to introduce the semidirect product (a topic usually first seen at the graduate level) in an undergrad...
متن کاملLagrangian Reduction, the Euler–Poincaré Equations, and Semidirect Products
There is a well developed and useful theory of Hamiltonian reduction for semidirect products, which applies to examples such as the heavy top, compressible fluids and MHD, which are governed by Lie-Poisson type equations. In this paper we study the Lagrangian analogue of this process and link it with the general theory of Lagrangian reduction; that is the reduction of variational principles. Th...
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تاریخ انتشار 2004