Some graded bialgebras related to Borcherds superalgebras (Q539531)

The author constructs a new kind of weak quantized enveloping algebras of Borcherds superalgebras associated with Borcherds-Cartan matrices with coloring matrices. The author proves that these new weak quantized enveloping algebras are noncommutative and noncocommutative bialgebras, and they have weak Hopf algebra structures if they satisfy some additional conditions. The author's construction is an analogue of the constructions that appeared in [\textit{S. Yang}, J. Math. Phys. 46, No. 7, 073502, 18 p. (2005; Zbl 1110.16047)] and [\textit{Z. Wu}, J. Math. Phys. 47, No. 6, 062108, 13 p. (2006; Zbl 1112.17025)] for quantized Borcherds superalgebras.