arXiv math/02110682002-11-04math.QAmath.RT

Covering Algebras II: Isomorphism of Loop Algebras

Bruce Allison, Stephen Berman, Arturo Pianzola

发表信息：: J. Reine Angew. Math. 571 (2004), 39-71

英文摘要：

This paper studies the loop algebras that arise from pairs consisting of a symmetrizable Kac-Moody Lie algebra $\g$ and a finite order automorphism $σ$ of $\g$. We obtain necessary and sufficient conditions for two such loop algebras to be isomorphic.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Isomorphism between super Yangian and quantum loop superalgebra. I

Following V. Toledano-Laredo and S. Gautam approach we construct isomorphism between super $\hbar$-Yangian $Y_{\hbar}(A(m,n))$ of special linear superalgebra and quantum loop superalgebra $U_{\hbar}(LA(m,n))$.

2018-04-18math.QA

A renormalized Riemann-Roch formula and the Thom isomorphism for the free loop space

Let E be a circle-equivariant complex-orientable cohomology theory. We show that the fixed-point formula applied to the free loopspace of a manifold X can be understood as a Riemann-Roch formula for the quotient of the formal group of E by a free cyclic subgroup. The quotient is not representable, but (locally at p) its p-torsion subgroup is, by a p-divisible group of height one greater than the formal group of E.

2001-01-14math-phmath.ATmath.MP

Free loop spaces and dihedral homology

We prove an $O(2)$-equivariant version of the Jones isomorphism relating the Borel $O(2)$-equivariant cohomology of the free loop space to the dihedral homology of the cochain algebra. We discuss polynomial forms and a variation of the de Rham isomorphism and use these to do a computation for the 2-sphere.

2016-08-29math.ATmath.QA

Iwahori-Hecke algebras for p-adic loop groups

This paper is a continuation of a previous paper in which the first two authors have introduced the spherical Hecke algebra and the Satake isomorphism for an untwisted affine Kac-Moody group over a non-archimedian local field. In this paper we develop the theory of the Iwahori-Hecke algebra associated to these same groups. The resulting algebra is shown to be closely related to Cherednik's double affine Hecke algebra. Furthermore, using these results, we give an explicit description of the affine Satake isomorphism, generalizing Macdonald's formula for the spherical function in the finite-dime…

2014-03-03math.NTmath.QAmath.RT

量子Grothendieck环与cluster代数之间的同构

Isomorphisms among quantum Grothendieck rings and cluster algebras

该研究为量子loop代数表示的量子Grothendieck环同构建立cluster理论诠释，得到monoidal范畴化定理的量子化，解决非simply-laced量子loop代数相关长期问题并建立量子$T$-系统，还给出同构对应的显式双有理变换替换公式。

2023-05-07math.QAmath.RAmath.RT

集合论杨-巴克斯特方程的二面体解

Dihedral solutions of the set theoretical Yang-Baxter equation

本文引入辫子二面体集和辫子三重性集来研究集合论杨-巴克斯特方程的解，并借助唯一2-可除Bruck环及指数3的交换Moufang环的对合给出完整分类与枚举。

2025-04-09math.QA

更多相关论文收起更多论文

量子环路群与通过Lyndon词的洗牌代数

Quantum loop groups and shuffle algebras via Lyndon words

本文通过环路词组合学推广有限型方法，研究量子环路群的PBW基，并证明Enriquez同态到椭圆代数三角退化为同构。

2024-03-14math.COmath.QAmath.RT

Van Den Bergh isomorphisms in String Topology

Let $M$ be a path-connected closed oriented $d$-dimensional smooth manifold and let ${\Bbbk}$ be a principal ideal domain. By Chas and Sullivan, the shifted free loop space homology of $M$, $H_{*+d}(LM)$ is a Batalin-Vilkovisky algebra. Let $G$ be a topological group such that $M$ is a classifying space of $G$. Denote by $S_*(G)$ the (normalized) singular chains on $G$. Suppose that $G$ is discrete or path-connected. We show that there is a Van Den Bergh type isomorphism $$ HH^{-p}(S_*(G),S_*(G))\cong HH_{p+d}(S_*(G),S_*(G)). $$ Therefore, the Gerstenhaber algebra $HH^{*}(S_*(G),S_*(G))$ is a …

2010-02-10math.ATmath.QA

Filtrations on graph complexes and the Grothendieck-Teichmüller Lie algebra in depth two

We establish an isomorphism between the Grothendieck-Teichmüller Lie algebra $\mathfrak{grt}_1$ in depth two modulo higher depth and the cohomology of the two-loop part of the graph complex of internally connected graphs $\mathsf{ICG}(1)$. In particular, we recover all linear relations satisfied by the brackets of the conjectural generators $σ_{2k+1}$ modulo depth three by considering relations among two-loop graphs. The Grothendieck-Teichmüller Lie algebra is related to the zeroth cohomology of M. Kontsevich's graph complex $\mathsf{GC}_2$ via T. Willwacher's isomorphism. We define a descendi…

2017-07-03math.QA

Free actions of compact quantum group on unital C*-algebras

Let F be a field, G a finite group, and Map(G,F) the Hopf algebra of all set-theoretic maps G->F. If E is a finite field extension of F and G is its Galois group, the extension is Galois if and only if the canonical map resulting from viewing E as a Map(G,F)-comodule is an isomorphism. Similarly, a finite covering space is regular if and only if the analogous canonical map is an isomorphism. In this paper we extend this point of view to actions of compact quantum groups on unital C*-algebras. We prove that such an action is free if and only if the canonical map (obtained using the underlying H…

2015-06-30math.ATmath.OAmath.QA