Boundary Solutions of the Classical Yang-Baxter Equation

Letters in Mathematical Physics

Volumn 40, Issue 4, 1997, Pages 337-353

  Gerstenhaber, M ^a   Giaquinto, A ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b MISSISSIPPI STATE UNIVERSITY   (United States)

Author keywords

Classical Yang Baxter equation; Maximal parabolic subalgebra; Quasi Frobenius Lie algebra

Indexed keywords

EID: 0000092033     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007363911649     Document Type: Article

References (13)

1. Belavin, A. A. and Drinfel'd, V. G.: Solutions of the classical Yang-Baxter equations for simple Lie algebras, Funct. Anal. Appl. 16 (1982), 159-180.
2. Chari, V. and Pressley, A.: A Guide to Quantum Groups, Cambridge University Press, New York, 1994.
3. Cremmer, E. and Gervais, J. L.: The quantum group structure associated with non-linearly extended Virasoro algebras, Comm. Math. Phys. 134 (1990), 619-632.
4. Elashvili, A, G.: Frobenius Lie algebras, Funct. Anal. Appl. 16 (1982), 94-95.
5. Elashvili, A. G.: Frobenius Lie algebras II, Proc. Math. Inst. Georgia Acad. Sci. (1986), 126-137 (Russian).
6. Fronsdal, C. and Galindo, A.: The universal T-matrix, Mathematical Aspects of Conformal and Topological Field Theories and Quantum Groups, Contemporary Mathematics 175, Amer. Math. Soc., Providence, R.I., 1994.
7. Fronsdal, C. and Galindo, A.: Deformations of multiparameter quantum gl(n), Lett. Math. Phys. 34 (1995), 25-36.
8. Fuchs, D.: Cohomology of Infinite Dimensional Lie Algebras, Consultants Bureau, New York, 1987.
9. Gerstenhaber, M., Giaquinto, A. and Schack, S. D.: Quantum symmetry, in: P. P. Kulish (ed.), Quantum Groups, Lecture Notes in Math. 1510, Springer, Berlin, New York, 1992, pp. 9-46.
10. Gerstenhaber, M., Giaquinto, A. and Schack, S. D.: Quantum groups, cohomology, and preferred deformations, in: S. Catto and A. Rocha (eds), Proc. XX Conference on Differential Geometric Techniques in Mathematical Physics, World Scientific, Singapore, 1992, pp. 529-538.
11. Gerstenhaber, M., Giaquinto, A. and Schack, S. D.: Construction of quantum groups from Belavin-Drinfel'd infinitesimals, in: A. Joseph and S. Shnider (eds), Quantum Deformation of Algebras and Their Representations, Israel Mathematical Conference Proc. 7, Amer. Math. Soc., Providence, 1993, pp. 45-64.
12. Stolin, A.: On rational solutions of Yang-Baxter equation for sl(n), Math. Scand. 69 (1991), 57-80.
13. Stolin, A.: Constant solutions of Yang-Baxter equation for sl(2) and sl(3), Math. Scand. 69 (1991), 81-88.