sklyanin algebra
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2017 ◽  
Vol 16 (05) ◽  
pp. 1750085 ◽  
Author(s):  
Kevin De Laet

In this paper, it is shown how the Heisenberg group of order 27 can be used to construct quotients of degenerate Sklyanin algebras. These quotients have properties similar to the classical Sklyanin case in the sense that they have the same Hilbert series, the same character series and a central element of degree 3. Regarding the central element of a three-dimensional Sklyanin algebra, a better way to view this using Heisenberg-invariants is shown.


2015 ◽  
Vol 9 (9) ◽  
pp. 2055-2119 ◽  
Author(s):  
Daniel Rogalski ◽  
Susan Sierra ◽  
J. Stafford
Keyword(s):  

2011 ◽  
Vol 226 (2) ◽  
pp. 1433-1473 ◽  
Author(s):  
D. Rogalski
Keyword(s):  

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Andrey Smirnov

AbstractNew trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl(N;?)-case is discussed.


2005 ◽  
Vol 38 (35) ◽  
pp. 7629-7659 ◽  
Author(s):  
H Boos ◽  
M Jimbo ◽  
T Miwa ◽  
F Smirnov ◽  
Y Takeyama

2001 ◽  
Vol 16 (26) ◽  
pp. 1711-1725
Author(s):  
V. A. DOLGUSHEV

A two-dimensional integrable system being a deformation of the rational Calogero–Moser system is constructed via the symplectic reduction, performed with respect to the Sklyanin algebra action. We explicitly resolve the respective classical equations of motion via the projection method and quantize the system.


2000 ◽  
Vol 7 (4) ◽  
pp. 689-700 ◽  
Author(s):  
G. Khimshiashvili ◽  
R. Przybysz

Abstract 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.


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