Differential geometry of the Lie algebra of the quantum plane

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ÇELİK S., ÇELİK S.

CZECHOSLOVAK JOURNAL OF PHYSICS, vol.55, no.4, pp.463-471, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 4
  • Publication Date: 2005
  • Doi Number: 10.1007/s10582-005-0052-8
  • Journal Name: CZECHOSLOVAK JOURNAL OF PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.463-471
  • Yıldız Technical University Affiliated: Yes

Abstract

We present a differential calculus on the extension of the quantum plane obtained by considering that the (bosonic) generator x is invertible and by working with polynomials in In x instead of polynomials in x. We construct the quantum Lie algebra associated with this extension and obtain its Hopf algebra structure and its dual Hopf algebra.