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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 187, Number 2, Pages 297–309
DOI: https://doi.org/10.4213/tmf9072
(Mi tmf9072)
 

This article is cited in 2 scientific papers (total in 2 papers)

Ideals generated by traces in the algebra of symplectic reflections $H_{1,\nu_1,\nu_2}(I_2(2m))$

S. E. Konsteinab, I. V. Tyutinac

a Tamm Theory Department, Lebedev Physical Institute, RAS, Moscow, Russia
b Al Farabi Science Research Institute for Experimental and Theoretical Physics, Kazakhstan National University, Almaty, Kazakhstan
c Tomsk State Pedagogical University, Tomsk, Russia
Full-text PDF (523 kB) Citations (2)
References:
Abstract: The associative algebra of symplectic reflections $\mathcal H:=H_{1,\nu_1,\nu_2} (I_2(2m))$ based on the group generated by the root system $I_2(2m)$ depends on two parameters, $\nu_1$ and $\nu_2$. For each value of these parameters, the algebra admits an $m$-dimensional space of traces. A trace $\operatorname{tr}$ is said to be degenerate if the corresponding symmetric bilinear form $B_{\operatorname{tr}}(x,y)=\operatorname{tr}(xy)$ is degenerate. We find all values of the parameters $\nu_1$ and $\nu_2$ for which the space of traces contains degenerate traces and the algebra $\mathcal H$ consequently has a two-sided ideal. It turns out that a linear combination of degenerate traces is also a degenerate trace. For the $\nu_1$ and $\nu_2$ values corresponding to degenerate traces, we find the dimensions of the space of degenerate traces.
Keywords: algebra of symplectic reflections, ideal, trace, supertrace, Coxeter group, group algebra.
Funding agency Grant number
Russian Foundation for Basic Research 14-02-0117
14-01-00489
Ministry of Education and Science of the Republic of Kazakhstan 3106/ГФ4
The research of S. E. Konstein is supported in part by the Russian Foundation for Basic Research (Grant No. 14-02-01171) and the Ministry of Education and Science, Republic of Kazakhstan (Grant No. 3106/GF4). The research of I. V. Tyutin is supported in part by the Russian Foundation for Basic Research (Grant No. 14-01-00489).
Received: 19.10.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 187, Issue 2, Pages 706–717
DOI: https://doi.org/10.1134/S004057791605007X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. E. Konstein, I. V. Tyutin, “Ideals generated by traces in the algebra of symplectic reflections $H_{1,\nu_1,\nu_2}(I_2(2m))$”, TMF, 187:2 (2016), 297–309; Theoret. and Math. Phys., 187:2 (2016), 706–717
Citation in format AMSBIB
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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