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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
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.
Received: 19.10.2015
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
Linking options:
https://www.mathnet.ru/eng/tmf9072https://doi.org/10.4213/tmf9072 https://www.mathnet.ru/eng/tmf/v187/i2/p297
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