3 The Poincaré - Birkhoff - Witt Theorem for Super Yangians
نویسنده
چکیده
Here we describe a Gauss decomposition of the Yangian Y (glm|n) of the general linear Lie superalgebra. This gives a connection between this Yangian and the Yangian of the classical Lie superalgebra Y (A(m− 1, n− 1)) defined and studied in papers by Stukopin. We also show that the coefficients of the quantum Berezinian generate the centre of the Yangian Y (glm|n). This is a conjecture of Nazarov dating back to 1991. Such Gauss decompositions have already been studied for the Yangian Y (gln) in papers by Brundan and Kleshchev, and Crampé, as well as for the super-Yangian Y (gl1|1) in the work of Jin-fang Cai, Guo-xing Ju, Ke Wu and Shi-kun Wang.
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