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Il Nuovo Cimento B (1971-1996)

, Volume 105, Issue 1, pp 1–12 | Cite as

New realization of the loop algebras and their indecomposable modules

  • Chang-Pu Sun
  • Hong-Chen Fu
Article

Summary

A new realization of the loop algebra Ĝ (untwisted affine Kac-Moody algebra) is given on the enveloping field\(\bar \Omega \) of the Bose algebraK. By making use of this new realization nontrivial infinite-dimensional indecomposable representations and finite-dimensional representations ofĜ are constructed on\(\bar \Omega \) and its quotient spaces. Finally, as an explicit example, the loop algebra\(\widehat{SU}(2)\) associated with Lie algebraSU(2) is discussed in detail.

Keywords

PACS 03.65.Fd Algebraic methods 

Новая реализация алгебры петель и неприводимые модули

Резюме

Предлагается новая реализация алгебры петельĜ (раскрученная аффинная алгебра Как-Муди) на огибающем поле\(\bar \Omega \) алгебры Бозе κ. Используя эту новую реализацию, конструируются нетривиальные бесконечномерные неприводимые представления и конечномерные представленияĜ на\(\bar \Omega \) иих частные пространства. В заключение, подробно обсуъдается пример алгебры петель\(\widehat{SU}(2)\), связанной с алгеброй ЛиSU(2).

Riassunto

Si dà una nuova realizzazione dell’algebra ad ansaĜ (algebra di Kac-Moody affine non intrecciata) sul campo inviluppante\(\bar \Omega \) dell’algebra di BoseK. Usando questa nuova realizzazione si elaborano rappresentazioni non scomponibili a dimensioni infinite non triviali e rappresentazioni a dimensioni finite diĜ su\(\bar \Omega \) e i suoi spazi quozienti. Infine si discute in dettaglio, come esempio esplicito, l’algebra ad ans\(\widehat{SU}(2)\) associata all’algebra di LieSU(2).

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Copyright information

© Società Italiana di Fisica 1990

Authors and Affiliations

  • Chang-Pu Sun
    • 1
  • Hong-Chen Fu
    • 1
  1. 1.Physics DepartmentNortheast Normal UniversityChangchen, Jilin ProvinceThe People’s Republic of China

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