arXiv subjects

Masamune Hattori

Publications and source records attributed to Masamune Hattori.

3 recordsLinked to original sources

arXiv2025

On the Hopf superalgebra of symmetric functions in superspace

We introduce a superspace analogue of combinatorial Hopf algebras (Aguiar-Bergeron-Sottile, 2006), and show that the Hopf superalgebra of quasi-symmetric (resp. symmetric) functions in superspace (Fishel-Lapointe-Pinto, 2019) is a terminal object in the category of all (resp. cocommutative) combinatorial Hopf superalgebras. We also introduce a superspace analogue of chromatic symmetric functions of graphs (Stanley, 1995) using the chromatic Hopf superalgebra of two-colored graphs.

math.CO↗

arXiv2024

Examples of solvable and nilpotent finite quantum groups

We prove the solvability and nilpotency of Kac--Paljutkin's finite quantum group and Sekine quantum groups and we classify the solvable series of Kac--Paljutkin's finite quantum group via Cohen--Westreich's Burnside theorem. Some semisimple quasitriangular Hopf algebras of dimensions $2pq$ are also studied. In Appendix A, we give a direct computation of the universal $R$-matrices for Kac--Paljutkin's $8$-dimensional finite quantum group.

math.QA↗

arXiv2022

A dynamical analogue of Ding-Iohara quantum algebras

We introduce a family of dynamical Hopf algebroids $U_{q,p}(g,X_l)$ depending on a complex parameter $q$, a formal parameter $p$, a set $g$ of structure functions satisfying the so-called Ding-Iohara condition, and a finite root system of type $X_l$. If $g$ is set to be certain theta functions, then our family recovers the elliptic algebras $U_{q,p}(\widehat{\mathfrak{g}})$ for untwisted affine Lie algebras $\widehat{\mathfrak{g}}$ studied by Konno (1998, 2009), Jimbo-Konno-Odake-Shiraishi (1999) and Farghly-Konno-Oshima (2014). Also, taking the limit $p \to 0$ in the case $X_l=A_l$, we recover the Hopf algebras $U_q(\overline{g},A_l)$ of type $A_l$ with structure functions $\overline{g} := \lim_{p \to 0} g$, introduced by Ding-Iohara (1998) as a generalization of Drinfeld quantum affine algebras. Thus, our Hopf algebroid $U_{q,p}(g,X_l)$ can be regarded as a dynamical analogue of the Ding-Iohara quantum algebras. As a byproduct, we obtain an extension of the Ding-Iohara quantum algebras to those of non-simply-laced type.

math.QA↗