A NEW QUANTUM SUPERGROUP AND ITS GAUSS DECOMPOSITION


Çelik S.

REPORTS ON MATHEMATICAL PHYSICS, vol.88, no.2, pp.259-269, 2021 (Journal Indexed in SCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 88 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.1016/s0034-4877(21)00073-2
  • Journal Name: REPORTS ON MATHEMATICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.259-269
  • Keywords: quantum superspaces, Hopf superalgebra, Gauss decomposition, DEFORMATION

Abstract

We get a new quantum supergroup (Hopf superalgebra), denoted by GL(q) (211), by using the standard method (the RU-relation) with an R-matrix which is a solution of the quantum Yang- Baxter equation. We give the Gauss decomposition of a matrix in GL(q) (211) and considering the three matrices in the decomposition in pairs, we show that two superalgebras formed by matrix elements of these matrices are Hopf superalgebras.