Representations of Algebras Defined by a Multiplicative Relation and Corresponding to the Extended Dynkin Graphs $\tilde{D}_4, \tilde{E}_6, \tilde{E}_7, \tilde{E}_8$

• Date: 2012
• Main Authors: Livins'kyi, I. V., Radchenko, D. V., Лівінський, І. В., Радченко, Д. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2689
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We describe, up to unitary equivalence, all $k$-tuples $(A_1, A_2,..., A_k)$ of unitary operators such that $A^{n_i}_i = I$ for $i = \overline{1, k}$ and $A_1 A_2 ... A_k = \lambda I$, where the parameters $(n_1,... ,n_k)$ correspond to one of the extended Dynkin diagrams $\tilde{D}_4, \tilde{E}_6...