Self-adjoint representations in Hilbert space of a family of quadratic algebras constructed by E. K. Sklyanin are studied. Complete sets of classes of unitary equivalence of irreducible representations are obtained for algebras that correspond to second-order points of elliptic curves.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
E. K. Sklyanin, “On some algebraic structures connected with the Yang-Baxter equation,” Funkts. Anal. Prilozhen.,16, No. 4, 27–34 (1982).
E. K. Sklyanin, “On some algebraic structures connected with the Yang-Baxter equation. Representations of the quantum algebra,” Funkts. Anal. Prilozhen.,17, No. 4, 34–48 (1983).
A. M. Vershik, “Algebras with quadratic relations,” in: Spectral Theory of Operators and Infinite-Dimensional Analysis [in Russian], Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1984), pp. 32–57.
S. A. Kruglyak, “Representations of a quantum algebra connected with the Yang-Baxter equation,” in: Spectral Theory of Operators and Infinite-Dimensional Analysis [in Russian], Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1984), pp. 111–120.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 11, pp. 1567–1574, November, 1991.
About this article
Cite this article
Bespalov, Y.N. On self-adjoint representations of the sklyanin algebras. Ukr Math J 43, 1458–1465 (1991). https://doi.org/10.1007/BF01067287
- Hilbert Space
- Irreducible Representation
- Elliptic Curf
- Quadratic Algebra
- Sklyanin Algebra