This article is cited in 2 papers

Belavin Elliptic $R$-Matrices and Exchange Algebras

A. V. Odesskii

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: We study Zamolodchikov algebras whose commutation relations are described by Belavin matrices defining a solution of the Yang–Baxter equation (Belavin $R$-matrices). Homomorphisms of Zamolodchikov algebras into dynamical algebras with exchange relations and also of algebras with exchange relations into Zamolodchikov algebras are constructed. It turns out that the structure of these algebras with exchange relations depends substantially on the primitive $n$th root of unity entering the definition of Belavin $R$-matrices.

UDC: 517

Received: 10.05.2001

DOI: 10.4213/faa178

 English version: Functional Analysis and Its Applications, 2002, 36:1, 49–61

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