Related papers: On autoduality of Drinfeld modules and Drinfeld mo…

We construct the Cartier duality equivalence for affine commutative group schemes $G$ whose coordinate ring is a flat Mittag-Leffler module over an arbitrary base ring $R$. The dual $G^\vee$ of $G$ turns out to be an ind-finite ind-scheme…

Let $A$ be a standardly stratified algebra over a field $K$ and $T$ a tilting module over $A$. Let $\Lambda^+$ be an indexing set of all simple modules in $A\lmod$. We show that if there is an integer $r\in\N$ such that for any…

We provide an analog of the Drinfeld quantum double construction in the context of crossed Hopf group coalgebras introduced by Turaev. We prove that, provided the base group is finite, the double of a semisimple crossed Hopf group coalgebra…

Let G be a split connected reductive group over a finite field F_q, and N its maximal unipotent subgroup. V. Drinfeld has introduced a remarkable partial compactification of the moduli stack of N-bundles on a smooth projective curve X over…

We introduce the notion of Drinfeld modular forms with $A$-expansions, where instead of the usual Fourier expansion in $t^n$ ($t$ being the uniformizer at `infinity'), parametrized by $n \in \mathbb{N}$, we look at expansions in $t_a$,…

Given an action $\varphi$ of of inverse semigroup $S$ on a ring $A$ (with domain of $\varphi(s)$ denoted by $D_{s^*}$) we show that if the ideals $D_e$, with $e$ an idempotent, are unital, then the skew inverse semigroup ring $A\rtimes S$…

We study rational points and torsion points on Drinfeld modular curves defined over rational function fields. As a consequence we derive a conjecture of Schweizer describing completely the torsion of Drinfeld modules of rank two over $\Bbb…

Let $(R, \Delta)$ be an odd form algebra. We show that the unitary Steinberg group $\mathrm{StU}(R, \Delta)$ is a crossed module over the odd unitary group $\mathrm U(R, \Delta)$ in two major cases: if the odd form algebra has a free…

Let ${U}_q(sl_2)$ be the quantized enveloping algebra associated to the simple Lie algebra $sl_2$. In this paper, we study the quantum double $D_q$ of the Borel subalgebra ${U}_q((sl_2)^{\leq 0})$ of ${U}_q(sl_2)$. We construct an analogue…

A Lefschetz module is a module over a graded algebra $A$ that satisfies analogues of Poincar\'{e} duality, the Hard Lefschetz property, and the Hodge--Riemann relations with respect to an open convex cone $\mathscr{K}$ in the degree one…

Let (S,L) be a Lie-Rinehart algebra over a commutative ring R. This article proves that, if S is flat as an R-module and has Van den Bergh duality in dimension n, and if L is finitely generated and projective with constant rank d as an…

In this paper, we develop a view of self-isogenous modular polynomials and the $\mathfrak{l}$-cyclic isogeny graph for CM Drinfeld modules of arbitrary rank $r$. On the computational side, we give an explicit procedure to construct the…

Given a finite group G acting as automorphisms on a ring A, the skew group ring A*G is an important tool for studying the structure of G-stable ideals of A. The ring A*G is G-graded, i.e.G coacts on A*G. The Cohen-Montgomery duality says…

The aim of this article is twofold: first, improve the multiplicity estimate obtained by the second author for Drinfeld quasi-modular forms; and then, study the structure of certain algebras of "almost-$A$-quasi-modular forms"

We generalize various properties of Yetter-Drinfeld modules over Hopf algebras to quasi-Hopf algebras. The dual of a finite dimensional Yetter-Drinfeld module is again a Yetter-Drinfeld module. The algebra $H_0$ in the category of…

We establish a connection between Drinfeld modules and rank-metric codes, focusing on the case of semifield codes. Our method constructs rank-metric codes from linear subspaces of endomorphisms of a Drinfeld module acting on torsion…

In this lecture we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. Our analysis is based on an approach to modular invariants using braided sector induction…

In this article, we prove the Hodge conjecture for a desingularization of the moduli space of rank 2, semi-stable, torsion-free sheaves with fixed odd degree determinant over a very general irreducible nodal curve of genus at least 2. We…

We define the notion of factorizable quasi-Hopf algebra by using a categorical point of view. We show that the Drinfeld double $D(H)$ of any finite dimensional quasi-Hopf algebra $H$ is factorizable, and we characterize $D(H)$ when $H$…

Let $H$ be a finite dimensional quasi-Hopf algebra over a field $k$ and ${\mathfrak A}$ a right $H$-comodule algebra in the sense of Hausser and Nill. We first show that on the $k$-vector space ${\mathfrak A}\ot H^*$ we can define an…