On root vectors and Lusztig bases for quantum Serre superalgebras of type~I (Q2719493)

The paper deals with a new structure of root vectors and Lusztig bases in quantum Serre superalgebras of type~I. Two methods of construction are indicated for the set of root vectors for every normal order in the system of positive roots \(\Delta^+\) of type~I. The first one is a preliminary construction of one such set associated with a specially chosen normal order in \(\Delta^+\) with a subsequent passage to the other sets of the root vectors by changing the normal order in the system \(\Delta^+\). In the second version an explicit method is shown for an immediate construction of the set of root vectors.