11 papers
Twisted quantum loop algebras via semi-derived Ringel-Hall algebras
Ming Lu, Shiquan Ruan
Twisted quantum loop algebras are a generalization of twisted quantum affine algebras in Drinfeld new presentation. The Hall algebras of Geigle--Lenzing's weighted projective lines…
Frobenius quotients, inflation categories and weighted projective lines
Xiao-Wu Chen, Qiang Dong, Shiquan Ruan
We propose the notion of Frobenius quotients between Frobenius exact categories. It turns out that any Frobenius quotient induces Frobenius quotients between the corresponding infl…
Double Hall-Littlewood symmetric polynomials
Jiayi Chen, Ming Lu, Shiquan Ruan
We establish a ring isomorphism between the derived Hall algebra of the Jordan quiver and the ring of double symmetric functions (i.e., the ring of symmetric polynomials in two set…
iQuantum groups and iHopf algebras II: dual canonical bases
Jiayi Chen, Ming Lu, Xiaolong Pan +2
Building on the iHopf algebra realization of quasi-split universal iquantum groups developed in a prequel, we construct the dual canonical basis for a universal iquantum group of a…
iQuantum groups and iHopf algebras I: foundation
Jiayi Chen, Ming Lu, Xiaolong Pan +2
We introduce the notion of iHopf algebra, a new associative algebra structure defined on a Hopf algebra equipped with a Hopf pairing. The iHopf algebra on a Borel quantum group end…
ACM tilting bundles on a Geigle-Lenzing projective plane of type
Jianmin Chen, Shiquan Ruan, Weikang Weng
Let be a Geigle-Lenzing projective plane of type and the category of coherent sheaves on . This paper is devoted to s…