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Letters in Mathematical Physics

, Volume 72, Issue 3, pp 197–210 | Cite as

Semi-Classical Twists for \({\mathfrak{sl}}_{3}\) and \({\mathfrak{sl}}_{4}\) Boundary r-Matrices of Cremmer–Gervais Type

  • M. Samsonov
Article

Abstract

We obtain explicit formulas for the semi-classical twists deforming the coalgebraic structure of \(U({\mathfrak{sl}}_{3})\) and \(U({\mathfrak{sl}}_{4})\). In rank 2 and 3 the corresponding universal R-matrices quantize the boundary r-matrices of Cremmer–Gervais type defining Lie Frobenius structures on the maximal parabolic subalgebras in \({\mathfrak{sl}}_{n}\).

Keywords

Generalized Jordanian r-matrices Cremmer–Gervais quantization semi-classical twists. 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Theoretical Department, Institute of PhysicsSt. Petersburg State UniversitySt. PetersburgRussia

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