Related papers: Introduction to twisted commutative algebras
Let $\Gamma$ be a generic subgroup of the multiplicative group $\mathbb{C}^*$ of nonzero complex numbers. We define a class of Lie algebras associated to $\Gamma$, called twisted $\Gamma$-Lie algebras, which is a natural generalization of…
The finite-dimensional symmetric algebras over an algebraically closed field, based on surface triangulations, motivated by the theory of cluster algebras, have been extensively investigated and applied. In particular, the weighted surface…
These three topics are an attempt to explicate some curiosities of the inverse problem of representation theory (i.e. having a set of operators to describe the "correct" algebraic object, which is represented by them) on simple examples…
This paper gives insight into intriguing connections between two apparently unrelated theories: the theory of skein modules of 3-manifolds and the theory of representations of groups into special linear groups of 2 by 2 matrices. Let R be a…
The goal of this article is to motivate and describe how Gromov-Witten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from Gromov-Witten theory have led to both conjectures and…
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
Using the representation theory of the subgroups SL_2(Z_p) of the modular group we investigate the induced fusion algebras in some simple examples. Only some of these representations lead to 'good' fusion algebras. Furthermore, the…
The main goal of the present paper is the construction of twisted generalized differential cohomology theories and the comprehensive statement of its basic functorial properties. Technically it combines the homotopy theoretic approach to…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…
This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct…
In this paper, we use the twisted regular representation theory of vertex operator algebras to construct bimodules over twisted Zhu algebras, extending Haisheng Li's work in untwisted scenarios. Moreover, a conjecture of Dong and Jiang on…
For simple twisted group algebra over a group $G$, if $G^{\shortmid}$ is Hall subgroup of $G$ then the semi-center is simple. Simple twisted groups algebras correspond to groups of central type. We classify all groups of central type of…
We define a GL-variety to be a (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms a polynomial representation. Such varieties have been used…
Group algebras of permutations have proved highly useful in solving a number of problems in large N gauge theories. I review the use of permutations in classifying gauge invariants in one-matrix and multi-matrix models and computing their…
In this paper we study classical deformations of diagrams of commutative algebras over a field of characteristic 0. In particular we determine several homotopy classes of DG-Lie algebras, each one of them controlling this above deformation…
We study the general twisted intertwining operators (intertwining operators among twisted modules) for a vertex operator algebra $V$. We give the skew-symmetry and contragredient isomorphisms between spaces of twisted intertwining operators…
We define the notion of whiskered categories and groupoids, showing that whiskered groupoids have a commutator theory. So also do whiskered $R$-categories, thus answering questions of what might be `commutative versions' of these theories.…
We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted…
In part I we introduce vertex rings, which bear the same relation to vertex algebras (or VOAs) as commutative, associative rings do to commutative, associative algebras over the complex numbers. We show that vertex rings are characterized…