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Representation of an algebra associated with the Dynkin graph \(\tilde E_7\)

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Abstract

We describe the structure of pairs of self-adjoint operators A and B whose spectra belong to the set {±1/2, ±3/2} and for which (A+B)2=I. Such pairs of operators determine a representation of a *-algebra \(A_{\tilde E_7 }\) associated with the extended Dynkin graph \(\tilde E_7\).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv

    V. L. Ostrovs’kyi

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  1. V. L. Ostrovs’kyi
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 9, pp. 1193–1202, September, 2004.

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Ostrovs’kyi, V.L. Representation of an algebra associated with the Dynkin graph \(\tilde E_7\) . Ukr Math J 56, 1417–1428 (2004). https://doi.org/10.1007/s11253-005-0125-7

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  • DOI: https://doi.org/10.1007/s11253-005-0125-7

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