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

  • I. V. Livins'kyi Iн-т математики НАН України, Київ
  • D. V. Radchenko Iн-т математики НАН України, Київ

Abstract

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 $\tilde{D}_4, \tilde{E}_6, \tilde{E}_7, \tilde{E}_8$, and $\lambda \in \mathbb{C}$ is a fixed root of unity.
Published
25.12.2012
How to Cite
Livins’kyiI. V., and RadchenkoD. V. “Representations of Algebras Defined by a Multiplicative Relation and Corresponding to the Extended Dynkin Graphs $\tilde{D}_4, \tilde{E}_6, \tilde{E}_7, \tilde{E}_8$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 12, Dec. 2012, pp. 1654-75, http://umj.imath.kiev.ua/index.php/umj/article/view/2689.
Section
Research articles