2022/07/14 by Pierre-Olivier Parisé, Parisé, Pierre-Olivier
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematics and Applications #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2207.06636
openalex publication_date 2022/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An involution of a real commutative algebra A is a real-linear homomorphism f : A → A such that f2 = Id. We show that there are six involutions of the algebra of bicomplex numbers, contrary to the actual number of four stated in the literature. We also characterize n-involutions satisfying the additional property fn = Id for some integer n ≥ 2. We show there are eight n-involutions and they occur only for n = 2 and n= 4. We use our result to give a new characterization of the invertible elements of the algebra of bicomplex numbers.