Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations (Q1175078)

The author shows that every compact semi-simple simply-connected Lie group \(G\) can be matched with some simply-connected Lie group \(G^*\), i.e., \(G\) and \(G^*\) act on each other with certain compatibility conditions so that there is a bicrossproduct group of \(G\) and \(G^*\). The proof involves a solution of the (modified) classical Yang-Baxter equation for the complexification of the Lie algebra of \(G\). The general construction is related to other work of the author on bicrossproducts and double cross product Hopf algebras [J. Algebra 130, No. 1, 17-64 (1990; Zbl 0694.16008); Isr. J. Math. 72, No. 1/2, 133-148 (1990; Zbl 0725.17015)].