Symplectic group

English

Etymology

So named by German mathematician Template:W, replacing previous confusing names. More at Template:M.

Noun

1. Template:Lb For given field F and positive integer n, the group of 2n×2n symplectic matrices with elements in F.
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   • 2001, G. Wassermann (translator), V. I. Arnol'd, A. B. Givental', Symplectic Geometry, V. I. Arnol'd, S. P. Novikov (editors), Dynamical Systems IV: Symplectic Geometry and its Applications, Springer, 2nd Edition, page 18,

     The exponential of an operator gives the exponential mapping $H\mapsto \text{exp}(H)=\sum H^k/k!$ of the space of Hamiltonian operators to the symplectic group. The symplectic group acts by conjugation on itself and on its Lie algebra.

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Usage notes

Can be denoted Sp(2n, F), although other notations are also used. In particular, what is denoted Sp(2n, F) in some texts appears as Sp(n, F) in others.

Derived terms

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Further reading

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