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- Karolinsky, E., et al.
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From dynamical to non-dynamical twists
- 2005
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In: Letters in Mathematical Physics. - : Springer Science and Business Media LLC. - 0377-9017 .- 1573-0530. ; 71:3, s. 173-178
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Journal article (peer-reviewed)abstract
- We provide a construction which gives a twisting element for a universal enveloping algebra starting from a certain dynamical twist. This construction is a quantization of the analogous quasi-classical process given in [Karolinsky and Stolin, Lett. Math. Phys. 60 (2002), 257-274]. In particular, we reduce the computation of the twisting element for the classical r-matrix constructed from the Frobenius algebra the maximal parabolic subalgebra of sl(n) related to the simple root alpha(n-1), to the computation of the universal dynamical twist for sl(n).
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- Karolinsky, E., et al.
(author)
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Irreducible highest weight modules and equivariant quantization
- 2007
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In: ADVANCES IN MATHEMATICS. - : Elsevier BV. - 0001-8708 .- 1090-2082. ; 211:1, s. 266-283
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Journal article (peer-reviewed)abstract
- We consider the relationship between the Shapovalov form on an previous termirreducible highestnext term weight module of a semisimple complex Lie algebra, fusion elements, and equivariant quantization. We also discuss some limiting properties of fusion elements
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- Pop, Iulia, 1976, et al.
(author)
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Rational solutions of CYBE for simple compact real Lie algebras
- 2007
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In: JOURNAL OF GEOMETRY AND PHYSICS. - : Elsevier BV. - 0393-0440. ; 57:5, s. 1379-1390
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Journal article (peer-reviewed)abstract
- In [A.A. Stolin, On rational solutions of YangBaxter equation for sl(n), Math. Scand. 69 (1991) 5780; A.A. Stolin, On rational solutions of YangBaxter equation. Maximal orders in loop algebra, Comm. Math. Phys. 141 (1991) 533548; A. Stolin, A geometrical approach to rational solutions of the classical YangBaxter equation. Part I, in: Walter de Gruyter & Co. (Ed.), Symposia Gaussiana, Conf. Alg., Berlin, New York, 1995, pp. 347357] a theory of rational solutions of the classical YangBaxter equation for a simple complex Lie algebra g was presented. We discuss this theory for simple compact real Lie algebras g. We prove that up to gauge equivalence all rational solutions have the form X(u, v) = u−v + t1 ^ t2 + · · · + t2n−1 ^ t2n, where denotes the quadratic Casimir element of g and {ti } are linearly independent elements in a maximal torus t of g. The quantization of these solutions is also emphasized.
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