论文标题
$ u_q（\ widehat {gl_2}）$的交替演示来自弗雷德尔 - 梅尔代数
The alternating presentation of $U_q(\widehat{gl_2})$ from Freidel-Maillet algebras
论文作者
论文摘要
一个无限的维代数表示$ \ bar {\ cal a} _q $，是$ u_q^+$的中心扩展的同构 - $ u_q（\ wideHat {sl_2}）$的正面部分是由Paul Terwilliger提出的。它提供了一个“交替”的庞加莱 - 鲍尔克霍夫 - 沃特（PBW）基础，除了已知的达米亚尼的PBW基础，它是从积极的根矢量构建的。在本文中，获得了$ \ bar {\ cal a} _q $的介绍，就弗雷德尔 - 梅尔类型代数而言。使用此演示文稿：（a）构建了$ \ bar {\ cal a} _q $的有限尺寸张量产品表示； （b）从$ \ bar {\ cal a} _q $发出的显式同构，到$ u_q（\ wideHat {gl_2}）$的某些drinfeld类型的“交替” subergebras; （c）在达米亚尼的根矢量方面，$ \ bar {\ cal a} _q $的所有生成器的$ u_q^+$中的图像获得了。 $ u_q（\ wideHat {sl_2}）$的新张量产品分解在drinfeld类型的“交替” subergebras方面。还详细介绍了$ \ bar {\ cal a} _q $的专业$ q \ rightarrow 1 $ of $ \ bar {\ cal a} _q $。在这种情况下，将演示作为非标准的杨巴克斯特代数。本文致力于保罗·特维格（Paul Terwilliger）的65岁生日。
An infinite dimensional algebra denoted $\bar{\cal A}_q$ that is isomorphic to a central extension of $U_q^+$ - the positive part of $U_q(\widehat{sl_2})$ - has been recently proposed by Paul Terwilliger. It provides an `alternating' Poincaré-Birkhoff-Witt (PBW) basis besides the known Damiani's PBW basis built from positive root vectors. In this paper, a presentation of $\bar{\cal A}_q$ in terms of a Freidel-Maillet type algebra is obtained. Using this presentation: (a) finite dimensional tensor product representations for $\bar{\cal A}_q$ are constructed; (b) explicit isomorphisms from $\bar{\cal A}_q$ to certain Drinfeld type `alternating' subalgebras of $U_q(\widehat{gl_2})$ are obtained; (c) the image in $U_q^+$ of all the generators of $\bar{\cal A}_q$ in terms of Damiani's root vectors is obtained. A new tensor product decomposition for $U_q(\widehat{sl_2})$ in terms of Drinfeld type `alternating' subalgebras follows. The specialization $q\rightarrow 1$ of $\bar{\cal A}_q$ is also introduced and studied in details. In this case, a presentation is given as a non-standard Yang-Baxter algebra. This paper is dedicated to Paul Terwilliger for his 65th birthday.
