caa a22 4500 469099208 CHVBK 20180323133040.0 cr unu---uuuuu 170328e19920301xx s 000 0 eng 10.1007/BF00402899 doi (NATIONALLICENCE)springer-10.1007/BF00402899 The uniqueness theorem for the universal R -matrix [Elektronische Daten] [S. Khoroshkin, V. Tolstoy] Up to now, the universal R-matrix for quantized Kac-Moody algebras Here the name \lsKac-Moody algebras\rs includes all semisimple finite-dimensional Lie algebras and all infinite-dimensional affine Kac-Moody algebras. is believed to be uniquely determined (for some ansatz) by properties of a quasi-cocommutativity and a quasi-triangularity. We prove here that the universal R-matrix (for the same ansatz) is uniquely determined by the property of the quasi-cocommutativity only. Thus, the quasi-triangular property (and the Yang-Baxter equation!) for the universal R-matrix is a consequence of the linear equation of the quasi-cocommutativity. The proof is based on properties of singular vectors in the tensor product of the Verma modules and the structure of extremal projector for quantized algebras. Explicit expressions of the universal R-matrix for quantized algebras U q (A inf1 sup(1) ) and U q (A inf2 sup(2) ) are given. Kluwer Academic Publishers, 1992 Khoroshkin S. Institute of New Technologies, Kirovogradskaya 11, 113587, Moscow, Russia aut Tolstoy V. Institute of Nuclear Physics, Moscow State University, 119899, Moscow, Russia aut Letters in Mathematical Physics Kluwer Academic Publishers 24/3(1992-03-01), 231-244 0377-9017 24:3<231 1992 24 11005 https://doi.org/10.1007/BF00402899 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00402899 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Khoroshkin S. Institute of New Technologies, Kirovogradskaya 11, 113587, Moscow, Russia aut NATIONALLICENCE 700 1- Tolstoy V. Institute of Nuclear Physics, Moscow State University, 119899, Moscow, Russia aut NATIONALLICENCE 773 0- Letters in Mathematical Physics Kluwer Academic Publishers 24/3(1992-03-01), 231-244 0377-9017 24:3<231 1992 24 11005 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer