We consider q-deformations of multiplicative hypertoric varieties, for q a non-zero element of an algebraically closed field of characteristic 0. We construct an algebra Dq of q-difference operators as a Heisenberg double in a braided monoidal category. We then focus on the case where q is specialized to a root of unity. In this setting, we use Dq to construct an Azumaya algebra on an l-twist of the multiplicative hypertoric variety, before showing that this algebra splits over the fibers of both the moment and resolution maps. Finally, we sketch a derived localization theorem for these Azumaya algebras.
Vertex Superalgebras for Hypertoric Varieties and 3d Abelian Gauge Theories
Research Institute for Mathematical Sciences, Kyoto University（京都大学数学科学研究所）；Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）；School of Mathematics, University of Edinburgh（爱丁堡大学数学学院）；DAMTP, University of Cambridge（剑桥大学应用数学与理论物理系）；Fachbereich Mathematik, Universität Hamburg（汉堡大学数学系）；Department of Mathematics and Statistics, Maynooth University（梅努斯大学数学与统计系）
Euler continuants in noncommutative quasi-Poisson geometry
它是由Boalch，欧拉连续出现李群值的时刻地图一类野生字符品种描述为模空间的点$\mathbb{P}^1$由Sibuya。此外，Boalch注意到，这些变种是最初由Calabi引入的某些Nakajima变种的乘法类似物，它们在两个顶点和$n$等向箭头上附着在双$Γ_n$上。在这篇文章中，我们更进一步，揭示了Sibuya品种可以理解使用非交换的准泊松几何建模的PRACTIAL $Γ_n$。我们证明了这些品种所携带的泊松结构，通过Kontsevich-Rosenberg原则，由一个明确的哈密顿双拟泊松代数定义在水平的$Γ_n$，使其非交换乘法矩映射的欧拉连续。这一结果推广了Van den Bergh的对偶$Γ_1$的Hamilton对偶拟Poisson代数.利用融合的方法，证明了附在$Γ_n$上的Hamilton双拟Poisson代数可以分解为附在$Γ_1$上的代数的$n$拷贝.
Quasi-Poisson varieties from double quasi-Poisson algebras in types $B,C,D$
Beijing Institute of Mathematical Sciences and Applications（北京国际数学研究中心）；Université Bourgogne Europe, CNRS, IMB UMR 5584（勃艮第欧洲大学，法国国家科学研究中心，IMB UMR 5584）
