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

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

Published:2013-05 Issue:12 Volume:64 Page:1865-1892
ISSN:0041-5995
Container-title:Ukrainian Mathematical Journal
language:en
Short-container-title:Ukr Math J

Author:

Livins’kyi I. V.,Radchenko D. V.

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

http://link.springer.com/content/pdf/10.1007/s11253-013-0757-y.pdf

Reference10 articles.

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2. A. S. Mellit, V. I. Rabanovich, and Yu. S. Samoilenko, “When is a sum of partial reflections equal to a scalar operator?” Funkts. Anal. Prilozhen., 38, Issue 2, 91–94 (2004).

3. V. L. Ostrovs’kyi and Yu. S. Samoilenko, “On spectral theorems for families of linearly connected self-adjoint operators with given spectra associated with extended Dynkin graphs,” Ukr. Mat. Zh., 58, No. 11, 1556–1570 (2006); English translation: Ukr. Math. J., 58, No. 11, 1768–1785 (2006).

4. P. R. Halmos and S. Kakutani, “Products of symmetries,” Bull. Amer. Math. Soc., 64, No. 3, 77–78 (1958).

5. M. Hladnik, M. Omladic, and H. Radjavi, “Products of roots of the identity,” Proc. Amer. Math. Soc., 129, 459–465 (2001).

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