Generalized Bicomplex Numbers and Lie Groups

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Karakuş S., Aksoyak F. K.

Advances in Applied Clifford Algebras, vol.25, no.4, pp.943-963, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 4
  • Publication Date: 2015
  • Doi Number: 10.1007/s00006-015-0545-x
  • Journal Name: Advances in Applied Clifford Algebras
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.943-963
  • Keywords: 30G35, 43A80, 53C40, 53C50
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

In this paper, we define the generalized bicomplex numbers and give some algebraic properties of them. Also, we show that some hyperquadrics in R4 and R24 are Lie groups by using generalized bicomplex number product and obtain Lie algebras of these Lie groups. Moreover, by using tensor product surfaces, we determine some special Lie subgroups of these hyperquadrics.