Two-dimensional R-matrices - Descendants of three-dimensional R-matrices

S. M. Sergeev

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Finite layers of three-dimensional models can be regarded as two-dimensional with complicated multi-stated weights. The tetrahedron equation in 3D provides the Yang-Baxter equation for this composite weights in 2D. Such solutions of the Yang-Baxter equation are constructed for the simplest operator solution of the tetrahedron equation. These R-matrices can be regarded as a special projection of universal R-matrix for some Drinfeld double Σ(A(1) r), associated with the affine algebra A(1) r. Usual R-matrix for Uq(A(1) r) is another projection of Σ(A(1) r).

Original languageEnglish
Pages (from-to)1393-1410
Number of pages18
JournalModern Physics Letters A
Volume12
Issue number19
DOIs
Publication statusPublished - 21 Jun 1997
Externally publishedYes

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R-matrix
Yang-Baxter Equation
Triangular pyramid
Three-dimensional
Projection
tetrahedrons
projection
three dimensional models
Composite
Algebra
algebra
Operator
operators
composite materials
Model

Cite this

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Two-dimensional R-matrices - Descendants of three-dimensional R-matrices. / Sergeev, S. M.

In: Modern Physics Letters A, Vol. 12, No. 19, 21.06.1997, p. 1393-1410.

Research output: Contribution to journalArticle

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