Related papers: On the Drinfeld formal group

We compute the rational stable homology of the automorphism groups of free nilpotent groups. These groups interpolate between the general linear groups over the ring of integers and the automorphism groups of free groups, and we employ…

Drinfeld orbifold algebras deform skew group algebras in polynomial degree at most one and hence encompass graded Hecke algebras, and in particular symplectic reflection algebras and rational Cherednik algebras. We introduce parametrized…

We generalize Quillen's $F$-isomorphism theorem, Quillen's stratification theorem, the stable transfer, and the finite generation of cohomology rings from finite groups to homotopical groups. As a consequence, we show that the category of…

Given a Hopf algebra $H$ and a counital $2$-cocycle $\mu$ on $H$, Drinfeld introduced a notion of twist which deforms an $H$-module algebra $A$ into a new algebra $A_\mu$. We show that when $A$ is a quadratic algebra, and $H$ acts on $A$ by…

In 1963, Greenberg proved that every finite group appears as the monodromy group of some morphism of Riemann surfaces. In this paper, we give two constructive proofs of Greenberg's result. First, we utilize free groups, which given with the…

Let (M, {\pi} ) be a Poisson manifold. A Poisson submanifold $P \in M$ gives rise to an algebroid $AP \rightarrow P$, to which we associate certain chomology groups which control formal deformations of {\pi} around P . Assuming that these…

We study sheaves of Lie-Rinehart algebras over locally ringed spaces. We introduce morphisms and comorphisms of such sheaves and prove factorization theorems for each kind of morphism. Using this notion of morphism, we obtain (higher)…

Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in detail. Their modular data - S, T and fusion matrices - are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain…

We develop a simple theory of Andr\'e-Quillen cohomology for commutative differential graded algebras over a field of characteristic zero. We then relate it to the homotopy groups of function spaces and spaces of homotopy self-equivalences…

Let $A$ be the coordinate ring of a projective smooth curve over a finite field minus a closed point. For a nontrivial ideal $I \subset A$, Drinfeld defined the notion of structure of level $I$ on a Drinfeld module. We extend this to that…

The Drinfeld twist is applyed to deforme the rank one orthosymplectic Lie superalgebra $osp(1|2)$. The twist element is the same as for the $sl(2)$ Lie algebra due to the embedding of the $sl(2)$ into the superalgebra $osp(1|2)$. The…

The goal of this paper is to study the absolute prismatic cohomology of $p$-adic formal schemes. We do so by recasting the notion of a prismatic crystal on $\mathrm{Spf}(\mathbf{Z}_p)$ in terms of quasicoherent sheaves on a geometric object…

We show that the natural map from the syntomification of a ring $R$ to the stack of $R$-algebra stacks is fully faithful, answering a question of Drinfeld, and we describe its essential image in terms of underlying monoid stacks. We also…

We define double (central and cocentral) extensions of Manin pairs introduced by Drinfeld, attached to curves and meromorphic differentials. We define ``infinite twistings'' of these pairs and quantize them in the $sl_{2}$ case, adapting…

We construct Drinfeld realisations for the quantum affine superalgebras associated with the osp(1|2n)^{(1)}, Sl(1|2n)^{(2)} and osp(2|2n)^{(2)} series of affine Lie superalgebras.

In this article, we investigate the representations of the Drinfeld doubles $D(R_{mn}(q))$ of the Radford Hopf algebras $R_{mn}(q)$ over an algebraically closed field $\Bbbk$, where $m>1$ and $n>1$ are integers and $q\in\Bbbk$ is a root of…

The question of whether the group $\mathbb{Q}_p \rtimes \mathbb{Q}_p^*$ is Hermitian has been stated as an open question in multiple sources in the literature, even as recently as a paper by R. Palma published in 2015. In this note we…

Via a construction due to V. Drinfel'd, we prove an equivalence of categories, generalizing the equivalence between commutative flat group schemes in characteristic $p$ with trivial Verschiebung and their Dieudonn\'e modules to group…

In this work we apply the Drinfel'd twist of Hopf algebras to the study of deformed quantum theories. We prove that, by carefully considering the role of the central extension, it is indeed possible to construct the universal enveloping…

We consider the algebra isomorphism found by Frenkel and Ding between the RLL and the Drinfeld realizations of $U_q(\widehat{gl(2)})$. After we note that this is not a Hopf algebra isomorphism, we prove that there is a unique Hopf algebra…