"Heisenberg group and Heisenberg algebra"의 두 판 사이의 차이

2009년 9월 10일 (목) 20:21 판

The automorphisms of the Heisenberg group (fixing its center) form the symplectic group

The Heisenberg group has an essentially unique irreducible unitary representation on a Hilbert space H with the center acting as a given nonzero constant (the content of the Stone-von Neumann theorem).

start with a Lattice \(<\cdot,\cdot>\)
make a vector space from it
Construct a Loop algbera
\(A\otimes\mathbb{C}[t,t^{-1}]\oplus\mathbb{C}c\)
\(\alpha(m)=\alpha\otimes t^m\)
Give a bracket
\([\alpha(m),\beta(n)]=m\delta_{m,-n}<\alpha,\beta>c\)
add a derivation \(d\)
\(d(\alpha(n))=n\alpha(n)\)
\(d(c)=0\)
define a Lie bracket
\([d,x]=d(x)\)

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 <h5 style="line-height: 2em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;">related items</h5>
-*   <br>[[Kac-Moody algebras]]<br>
+* [[half-integral weight modular forms|half-integral modular forms]]<br>
+* [[Kac-Moody algebras]]<br>
 * [[central extension of groups and Lie algebras|central extension of semisimple lie algebra]]<br>
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 * http://ko.wikipedia.org/wiki/
 * http://en.wikipedia.org/wiki/Heisenberg_algebra
+* http://en.wikipedia.org/wiki/Weyl_algebra
 * [http://en.wikipedia.org/wiki/Stone%E2%80%93von_Neumann_theorem http://en.wikipedia.org/wiki/Stone–von_Neumann_theorem]
 * http://en.wikipedia.org/wiki/