Related papers: Twisted divided powers and applications

Twisted symmetries, widely studied in the last decade, proved to be as effective as standard ones in the analysis and reduction of nonlinear equations. We explain this effectiveness in terms of a Lie-Frobenius reduction; this requires to…

The Toroidal Lie algebras are n variable genaralizations of Affine Kac-Moody Lie algebras. As in the affine Lie algebras there exists finite order auto= morphisms corresponding to Dynkin diagram automorphisms. The fixed point sub= algebras…

Let ${\mathcal A}$ be a generalized $q$-Weyl algebra, it is generated by $u$, $v$, $Z$, $Z^{-1}$ with relations $ZuZ^{-1}=q^2u$, $ZvZ^{-1}=q^{-2}v$, $uv=P\big(q^{-1}Z\big)$, $vu=P(qZ)$, where $P$ is a Laurent polynomial. A Hermitian form…

This note is to concern a generalization to the case of twisted coefficients of the classical theory of Abelian differentials on a compact Riemann surface. We apply the Dirichlet's principle to a modified energy functional to show the…

We study twisted derived equivalences for schemes in the setting of spectral algebraic geometry. To this end, we introduce the notion of a twisted equivalence and show that a twisted equivalence for perfect spectral algebraic stacks…

Inspired by the theory of p-adic differential equations, this paper introduces an analogous theory for q-difference equations over a local field, when |q|=1. We define some basic concepts, for instance the generic radius of convergence,…

Using $n$ finite order automorphisms on a simple complex Lie algebra we construct twisted $n$-toroidal Lie algebras. Thus obtaining Lie algebras wich have a rootspace decomposition. For the case $n=2$ we list certain simple Lie algebras and…

We study the existence of formal power series solutions to q-algebraic equations. When a solution exists, we give a sufficient condition on the equation for this solution to have a positive radius of convergence. We emphasize on the case…

We study the notion of twisted conjugacy separability (essentially introduced in our previous paper for a proof of twisted version of Burnside-Frobenius theorem) and some related properties. We give examples of groups with and without this…

We derive three identities of symmetry in two variables and eight in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by unramified roots of unity. The case…

We establish the $Q \widetilde{Q}$-systems for the twisted quantum affine algebras that were conjectured in arXiv:1606.05301. We develop the representation theory of Borel subalgebra of twisted quantum affine algebras and we construct their…

We define the $p^m$-curvature map on the sheaf of differential operators of level $m$ on a scheme of positive characteristic $p$ as dual to some divided power map on infinitesimal neighborhhods. This leads to the notion of $p^m$-curvature…

In this paper, we introduce novel concepts and establish a formal framework for twisted differential operators in the context of several variables. The focus is on twisted coordinates within Huber rings, which facilitate the construction of…

We describe the twisted doubling integrals of Cai-Friedberg-Ginzburg-Kaplan in a conceptual way. This also extends the construction to the quaternionic unitary groups. We carry out the unfolding argument uniformly in this article. To do so,…

We consider graded twisted Calabi-Yau algebras of dimension 3 which are derivation-quotient algebras of the form $A = \kk Q/I$, where $Q$ is a quiver and $I$ is an ideal of relations coming from taking partial derivatives of a twisted…

$q$-Yangians can be viewed both as quantum deformations of the loop algebras of upper triangular Lie algebras and deformations of the Yangian algebras. In this paper, we study the quantum affine algebra as a product of two copies of the…

Given an ideal $I$ in a commutative ring $A$, a divided power structure on $I$ is a collection of maps $\{\gamma_n \colon I \to A\}_{n \in \mathbb{N}}$, subject to axioms that imply that it behaves like the family $\{x \mapsto…

Positive twisted traces are mathematical objects that could be useful in computing certain parameters of superconformal field theories. The case when $\mathcal{A}$ is a $q$-Weyl algebra and $\rho$ is a certain antilinear automorphism of…

Let X be a smooth algebraic variety over a field of characteristic 0. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf O_X. These are stack-like versions of usual deformations. We prove that…

This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity. We show the interest of such algebras for fractional supersymmetric quantum mechanics, angular momentum theory and…