A two-parameter quantum group is obtained from the usual enveloping algebra by adding two commutative grouplike elements. In this paper, we generalize this procession further by adding commutative grouplike elements b...A two-parameter quantum group is obtained from the usual enveloping algebra by adding two commutative grouplike elements. In this paper, we generalize this procession further by adding commutative grouplike elements b（ik）, c（ik）, g（ik）, h（ik）（i ∈I, k = 1,..., mi） of a Hopf algebra H to the quantized enveloping algebra Uq（G） of a Borcherds superalgebra G defined by a symmetrizable integral Borcherds–Cartan matrix A =（aij）i,j∈I. Therefore, we define an extended Hopf superalgebra HUq（G）. We also discuss the basis and the grouplike elements of HUqG.展开更多
In this work, we show that the difference of a Hauptmodul for a genus zero group Γ_(0)(N) as a modular function on Y_(0)(N) × Y_(0)(N) is a Borcherds lift of type(2, 2). As applications, we derive the monster de...In this work, we show that the difference of a Hauptmodul for a genus zero group Γ_(0)(N) as a modular function on Y_(0)(N) × Y_(0)(N) is a Borcherds lift of type(2, 2). As applications, we derive the monster denominator formula like product expansions for these modular functions and certain Gross-Zagier type CM value formulas.展开更多
基金supported by NSFC(No.11171296)the Foundation of Zhejiang Provincial Educational Committee(No.Y201327644,No.FX2014082)the Natural Science Foundation of Zhejiang Province(No.LQ13A010018,No.LZ14A010001,No.LY15A010002)
基金Supported by National Natural Science Foundation of China(Grant No.11171296)the Foundation of Zhejiang Provincial Educational Committee(Grant Nos.Y201327644 and FX2014082)the Natural Science Foundation of Zhejiang Province(Grant Nos.Q13A01005 and LZ14A010001)
文摘A two-parameter quantum group is obtained from the usual enveloping algebra by adding two commutative grouplike elements. In this paper, we generalize this procession further by adding commutative grouplike elements b（ik）, c（ik）, g（ik）, h（ik）（i ∈I, k = 1,..., mi） of a Hopf algebra H to the quantized enveloping algebra Uq（G） of a Borcherds superalgebra G defined by a symmetrizable integral Borcherds–Cartan matrix A =（aij）i,j∈I. Therefore, we define an extended Hopf superalgebra HUq（G）. We also discuss the basis and the grouplike elements of HUqG.
基金supported by National Natural Science Foundation of China(Grant No.11901586)the Natural Science Foundation of Guangdong Province(Grant No.2019A1515011323)the Sun Yat-sen University Research Grant for Youth Scholars(Grant No.19lgpy244)。
文摘In this work, we show that the difference of a Hauptmodul for a genus zero group Γ_(0)(N) as a modular function on Y_(0)(N) × Y_(0)(N) is a Borcherds lift of type(2, 2). As applications, we derive the monster denominator formula like product expansions for these modular functions and certain Gross-Zagier type CM value formulas.
