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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

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Volume 7, Issue 4


On Generalized Sklyanin Algebras

G. Khimshiashvili
  • A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St., Tbilisi 380093, Georgia. E-mail:
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/ R. Przybysz
  • Department of Theoretical Physics, University of Lodz, Pomorska str. 149/153, Lodz 90-236, Poland. E-mail:
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Published Online: 2010-02-23 | DOI: https://doi.org/10.1515/GMJ.2000.689


A class of algebraic Poisson structures on R 4 is introduced which contains the well-known Sklyanin algebras. For this class, an effective algebraic method of computing Euler characteristics of Casimir levels is developed which enables us to compute them in the case of Sklyanin algebras. It is also shown that one may associate a finite graph with every generalized Sklyanin algebra. Some related results and open problems are also presented.

Key words and phrases:: Poisson structure; Sklyanin algebra; Casimir level; Euler characteristic; Petrovsky number

About the article

Received: 2000-09-18

Published Online: 2010-02-23

Published in Print: 2000-12-01

Citation Information: Georgian Mathematical Journal, Volume 7, Issue 4, Pages 689–700, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/GMJ.2000.689.

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