Heisenberg group and Heisenberg algebra

introduction

• start with a Lattice \(<\cdot,\cdot>\)
  
• make a vector space from it
  
• \([\alpha(m),\beta(n)]=m\delta_{m,-n}<\alpha,\beta>c\)
  
• add a derivation \(d\)
  \(d(\alpha(n))=n\alpha(n)\)
  \(d(c)=0\)
  
• define a Lie bracket
  \([d,x]=d(x)\)
  

 

 

 

 

 

related items

• Kac-Moody algebras
  

 

books

• 찾아볼 수학책
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

 

 

encyclopedia

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Heisenberg_algebra
• http://en.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• Princeton companion to mathematics(첨부파일로 올릴것)
  

 

blogs

• 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q=
• 트렌비 블로그 검색 http://www.trenb.com/search.qst?q=

 

articles

• 논문정리
• The Cover of June/July  2003  Volume 50  Issue 6 
  
  • Notices of AMS
• http://www.zentralblatt-math.org/zmath/en/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html

• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
• http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=