Ideals generated by traces in the algebra of symplectic reflections \({H_{1,{v_{1,}}{v_2}}}\left( {{I_2}\left( {2m} \right)} \right)\)
- Authors: Konstein S.E.1,2, Tyutin I.V.1,3
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Affiliations:
- Tamm Theory Department
- Al Farabi Science Research Institute for Experimental and Theoretical Physics
- Tomsk State Pedagogical University
- Issue: Vol 187, No 2 (2016)
- Pages: 706-717
- Section: Article
- URL: https://journals.rcsi.science/0040-5779/article/view/170586
- DOI: https://doi.org/10.1134/S004057791605007X
- ID: 170586
Cite item
Abstract
The associative algebra of symplectic reflections \(H: = {H_{1,{v_{1,}}{v_2}}}\left( {{I_2}\left( {2m} \right)} \right)\) based on the group generated by the root system I2(2m) depends on two parameters, ν1 and ν2. For each value of these parameters, the algebra admits an m-dimensional space of traces. A trace tr is said to be degenerate if the corresponding symmetric bilinear form Btr(x, y) = tr(xy) is degenerate. We find all values of the parameters ν1 and ν2 for which the space of traces contains degenerate traces and the algebra H consequently has a two-sided ideal. It turns out that a linear combination of degenerate traces is also a degenerate trace. For the ν1 and ν2 values corresponding to degenerate traces, we find the dimensions of the space of degenerate traces.
About the authors
S. E. Konstein
Tamm Theory Department; Al Farabi Science Research Institute for Experimental and Theoretical Physics
Author for correspondence.
Email: konstein@lpi.ru
Russian Federation, Moscow; Almaty
I. V. Tyutin
Tamm Theory Department; Tomsk State Pedagogical University
Email: konstein@lpi.ru
Russian Federation, Moscow; Tomsk
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