Derivations of generalized quaternion algebra

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Kızıl E., Alagöz Y.

TURKISH JOURNAL OF MATHEMATICS, vol.43, pp.2649-2657, 2019 (SCI-Expanded, Scopus, TRDizin)

  • Publication Type: Article / Article
  • Volume: 43
  • Publication Date: 2019
  • Doi Number: 10.3906/mat-1905-86
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2649-2657
  • Keywords: Derivation, quaternion, CONTROLLABILITY, SYSTEMS
  • Open Archive Collection: AVESIS Open Access Collection
  • Yıldız Technical University Affiliated: Yes

Abstract

The purpose of this paper is to determine derivations of the algebra H-alpha,H-beta of generalized quaternions over the reals and hence to obtain the algebra Der(H-alpha,H-beta) of derivations of H-alpha,H-beta. Once we know derivations we might decompose Der(H-alpha,H-beta) in terms of its inner and/or central derivations whenever they exist. Apart from Der(H-alpha,H-beta) we would also be able to obtain generalized derivations, which have been studied by analysts in the context of algebras of some normed spaces, and of prime and semiprime rings.