Poisson structures and star products on quasimodular forms

转置Novikov-泊松代数

Transposed Novikov-Poisson algebras

本文研究了转置Novikov-泊松代数的定义、结构及其与Novikov代数的关系，展示了其在张量积和导子中的应用，并探讨了其在单代数中的性质。

论 Kantor 积，II

On the Kantor product, II

本文研究乘法的 Kantor 平方与 Kantor 积，推广已有分类，并给出低维代数示例及构造新 transposed Poisson、Poisson-Novikov 代数和分类相关结构的方法。

The global extension problem, crossed products and co-flag non-commutative Poisson algebras

Let $P$ be a Poisson algebra, $E$ a vector space and $π: E \to P$ an epimorphism of vector spaces with $V = {\rm Ker} (π)$. The global extension problem asks for the classification of all Poisson algebra structures that can be defined on $E$ such that $π: E \to P$ becomes a morphism of Poisson algebras. From a geometrical point of view it means to decompose this groupoid into connected components and to indicate a point in each such component. All such Poisson algebra structures on $E$ are classified by an explicitly constructed classifying set ${\mathcal G} {\mathcal P} {\mathcal H}^{2} \, (P…

泊松CGL扩张的突变矩阵

Mutation matrices from Poisson CGL extensions

研究对称泊松CGL扩张，通过矩阵乘积和按元素描述，给出Goodearl - Yakimov理论中一族突变矩阵的显式公式，揭示其具有相容簇结构。

Hochschild products and global non-abelian cohomology for algebras. Applications

Let $A$ be a unital associative algebra over a field $k$, $E$ a vector space and $π: E \to A$ a surjective linear map with $V = {\rm Ker} (π)$. All algebra structures on $E$ such that $π: E \to A$ becomes an algebra map are described and classified by an explicitly constructed global cohomological type object ${\mathbb G} {\mathbb H}^{2} \, (A, \, V)$. Any such algebra is isomorphic to a Hochschild product $A \star V$, an algebra introduced as a generalization of a classical construction. We prove that ${\mathbb G} {\mathbb H}^{2} \, (A, \, V)$ is the coproduct of all non-abelian cohomologies …

代数结构的仿射化：泊松代数

Affinization of algebraic structures: Poisson algebras

研究泊松代数概念的仿射化，即泊松仿代数，其包含仿射空间、结合双仿射乘法和双仿射李括号，阐述了与泊松代数的关系并研究低维示例。

Double Poisson structures on finite dimensional semi-simple algebras

We give a description of the bimodule of double derivations DDer(S) of a finite dimensional semi-simple algebra S and its double Schouten bracket in terms of a quiver. This description is used to determine which degree two monomials in T_SDDer(S) induce double Poisson brackets on S. In case S = C^n, a criterion for any degree two element to give a double Poisson bracket is deduced. For S = C^n and S' = C^m, the induced Poisson bracket on the variety of isomorphism classes of semi-simple representations iss_n(S*T) of the free product S*T is given.

什么是双星积？

What is a double star-product?

本文研究了双泊松括号的变形量子化问题，提出了一种在代数表示空间上诱导星积的结构，并给出了一个具体例子和双形式定理。

Discriminants of Taft algebra smash products and applications

A general criterion is given for when the center of a Taft algebra smash product is the fixed ring. This is applied to the study of the noncommutative discriminant. Our method relies on the Poisson methods of Nguyen, Trampel, and Yakimov, but also makes use of Poisson Ore extensions. Specifically, we fully determine the inner faithful actions of Taft algebras on quantum planes and quantum Weyl algebras. We compute the discriminant of the corresponding smash product and apply it to compute the Azumaya locus and restricted automorphism group.