Abstract
In this paper, we define the generalized bicomplex numbers and give some algebraic properties of them. Also, we show that some hyperquadrics in \({\mathbb{R}^{4}}\) and \({\mathbb{R}_{2}^{4}}\) 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.
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Karakuş, S.Ö., Aksoyak, F.K. Generalized Bicomplex Numbers and Lie Groups. Adv. Appl. Clifford Algebras 25, 943–963 (2015). https://doi.org/10.1007/s00006-015-0545-x
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DOI: https://doi.org/10.1007/s00006-015-0545-x