On rational extension of Heisenberg algebra
英文摘要：
Construction of rational extension for Heisenberg algebra with one pair of generators is discussed.
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
限制 Heisenberg 李超代数的限制中心扩张
Restricted Central Extensions of Restricted Heisenberg Lie Superalgebras
该研究在特征 p > 2 的代数闭域上，利用平凡系数的普通 1、2 阶上同调计算限制 Heisenberg 李超代数的限制 2 阶上同调，并刻画其限制一维中心扩张。
math.RA
An extension of a $q$-deformed Heisenberg algebra and its Lie polynomials
Let $\mathbb{F}$ be a field, and fix a $q\in\mathbb{F}$. The $q$-deformed Heisenberg algebra $\mathcal{H}(q)$ is the unital associative algebra over $\mathbb{F}$ with generators $A$, $B$ and a relation which asserts that $AB - qBA$ is the multiplicative identity in $\mathcal{H}(q)$. We extend $\mathcal{H}(q)$ into an algebra $\mathcal{R}(q)$ defined by generators $A$, $B$ and a relation which asserts that $AB-qBA$ is central in $\mathcal{R}(q)$. We identify all elements of $\mathcal{R}(q)$ that are Lie polynomials in $A$, $B$.
math.RA
Deformed higher rank Heisenberg-Virasoro algebras
In this paper, we study a class of infinitesimal deformations of the centerless higher rank Heisenberg-Virasoro algebras. Explicitly, the universal central extensions, derivations and isomorphism classes of these algebras are determined.
math.RA
某些量子海森堡代数的同调性质
Homological properties of some quantum Heisenberg algebras
本文研究一类依赖参数q和多项式f、g的量子广义海森堡代数的Koszul、Artin-Schelter正则与Calabi-Yau等同调性质，并证明在特定条件下这些代数满足上述性质。
math.RA
有理向量场的李维利可积性：代数扩张的情况
Liouvillian integrability of rational vector fields: The case of algebraic extensions
Universitat Politècnica de Catalunya (EPSEB)（加泰罗尼亚理工大学）；Fachgruppe Mathematik, RWTH Aachen（亚琛工业大学数学系）
本文研究了有理向量场在代数扩张下的李维利可积性，证明了存在例外向量场，并在三维空间中给出了显式构造。
math.RA
Rational Extensions of C(X) via Hausdorff Continuous Functions
The ring operations and the metric on $C(X)$ are extended to the set $\mathbb{H}_{nf}(X)$ of all nearly finite Hausdorff continuous interval valued functions and it is shown that $\mathbb{H}_{nf}(X)$ is both rationally and topologically complete. Hence, the rings of quotients of $C(X)$ as well as their metric completions are represented as rings of Hausdorff continuous functions.
math.CAmath.RA
更多相关论文收起更多论文
On Extensions of Rational Modules
We investigate when the categories of all rational $A$-modules and of finite dimensional rational modules are closed under extensions inside the category of $C^*$-modules, where $C^*$ is the cofinite topological completion of $A$. We give a complete characterization of these two properties, in terms of a topological and a homological condition. We also give connections to other important notions in coalgebra theory such as coreflexive coalgebras. In particular, we are able to generalize many previously known partial results and answer some questions in this direction, and obtain large classes …
math.CTmath.RAmath.RT
On a radical extension of the field of rational functions in several variables
Let $F$ be a field and let $F(X_1,\dots,X_n)$ be the field of rational functions in $n$ variables $X_1,\dots,X_n$ over $F$. Let $T=X_1+\cdots+X_n\in F(X_1,\dots,X_n)$ and let $m$ be a positive integer such that $\text{char}\,F\nmid m$. Is it possible to express each $X_i$ as a rational function in $X_1^m\dots,X_n^m$ and $T$ over $F$? It is not difficult to prove that this can be done but it is another matter to show how this is done. We answer the above question affirmatively with a nonconstructive proof and a constructive proof.
math.RA
限制扭曲海森堡李代数的上同调
Cohomology of Restricted Twisted Heisenberg Lie Algebras
本文研究了限制扭曲海森堡李代数的上同调，通过谱序列计算平凡上同调，并给出了中心扩张的显式公式。
math.RA
二面体扩张的范数一环面的合理性问题
Rationality problem for norm one tori for dihedral extensions
本文利用Endo与Miyata及Endo的定理，完整解决了Galois闭包为二面体扩张的范数一环面的合理性（稳定等价）问题，并在附录中细化了稳定有理情形的证明。
math.AGmath.NTmath.RA
