Сommutative сomplex algebras of the second rank with unity and some cases of plane orthotropy. I

• Datum: 2018
• Hauptverfasser: Gryshchuk, S. V., Грищук, С. В.
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2018
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/1617
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

Among all two-dimensional algebras of the second rank with unity $e$ over the field of complex numbers $C$, we find a semisimple algebra $B_0 = \{ c_1e + c_2\omega: c_k \in C, k = 1, 2\} , \omega^2 = e$, containing bases $(e_1, e_2)$, such that $e^4_1 + 2pe^2_1e^2_2 + e^4_2 = 0$ for every fixed $p...