arXiv subjects

Maozhou Huang

Publications and source records attributed to Maozhou Huang.

5 recordsLinked to original sources

arXiv2026

Biquantization of the necklace Lie bialgebra

For the double of a quiver, the works of Ginzburg, Bocklandt-Le Bruyn and Schedler show that its closed paths, called the necklaces, have a natural Lie bialgebra structure. Schedler also constructed,in [Int. Math. Res. Notices, 2005 (12), 725-760], a Hopf algebra that quantizes this Lie bialgebra. In this paper, we pursue one more step in this direction by constructing its biquantization, in the sense of Turaev [Ann. Sci. École Norm. Sup. (4) 24 (1991), no. 6, 635-704].

math.RA↗

arXiv2026

Algebraic $K$-theory, cohomotopy $K$-groups, and Koszul duality

Let $A$ be an augmented differential graded algebra over a field $k$ of characteristic zero, and let $A^!=\mathbf{R}\mathrm{Hom}_A(k,k)$ be its Koszul dual algebra. Blumberg and Mandell showed that, under some finiteness conditions of $A$, the derived Koszul duality provides an equivalence between the $K$-theory $K(\mathrm{thick}_A(k))$ of the triangulated thick subcategory generated by $k$ and the $K$-theory $K(A^!)$ of the derived category of perfect $A^!$-modules. Combining this equivalence with the Jones-Goodwillie Chern character and the Jones-McCleary isomorphism, we obtain that the $K$-groups $K_n(\mathrm{thick}_A(k))$ are a concrete candidate for Loday's conjectural contravariant $K$-groups.

math.KT↗

arXiv2025

Deformation and quantization of the Loday-Quillen-Tsygan isomorphism for Calabi-Yau categories

For an associative algebra $A$, the famous theorem of Loday, Quillen and Tsygan says that there is an isomorphism between the graded symmetric product of the cyclic homology of $A$ and the Lie algebra homology of the infinite matrices $\mathfrak{gl}(A)$, as commutative and cocommutative Hopf algebras. This paper aims to study a deformation and quantization of this isomorphism. We show that if $A$ is a Koszul Calabi-Yau algebra, then the primitive part of the Lie algebra homology $\mathrm{H}_\bullet (\mathfrak{gl}(A))$ has a Lie bialgebra structure which is induced from the Poincaré duality of $A$ and deforms $\mathrm{H}_\bullet (\mathfrak{gl}(A))$ to a co-Poisson bialgebra. Moreover, there is a Hopf algebra which quantizes such a co-Poisson bialgebra, and the Loday-Quillen-Tsygan isomorphism lifts to the quantum level, which can be interpreted as a quantization of the tangent map from the tangent complex of $\mathrm{BGL}$ to the tangent complex of K-theory.

math.RA↗

arXiv2024

Ramification of Tate modules for rank $2$ Drinfeld modules

In this paper, we study the ramification of extensions of a function field generated by division points of rank 2 Drinfeld modules. Also conductors of certain rank 2 Drinfeld modules are defined as analogues of those for elliptic curves. A calculation of these conductors allows us to show an analogue of Szpiro's conjecture under a certain limited situation.

math.NT↗

arXiv2023

On successive minimal bases of division points of Drinfeld modules

We define successive minimal bases (SMBs) for the space of $u^{n}$-division points of a Drinfeld $\mathbb{F}_{q}[t]$-module over a local field, where $u$ is a finite prime of $\mathbb{F}_{q}[t]$ and $n$ is a positive integer. These SMBs share similar properties to those of SMBs of the lattices associated to Drinfeld modules. We study the relations between these SMBs and those of the lattices. Finally, we apply the relations to study the explicit wild ramification subgroup action on an SMB of the space of $u^{n}$-division points and show the function field analogue of Szpiro's conjecture for rank $2$ Drinfeld modules under a certain limited situation.

math.NT↗