华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (6): 1-13.

• 应用数学与基础数学 •    下一篇

单位根处的某些单Uq(gln)}-模的Krull--Schmidt分解

顾海霞, 王建磐   

  1. 华东师范大学~~数学系, 上海 200241
  • 收稿日期:2013-08-01 修回日期:2013-10-01 出版日期:2013-11-25 发布日期:2014-01-13

Krull--Schmidt decomposition of the tensor  products of certain simpleUq(gln)-modules at a root of unity

GU Hai-xia, WANG Jian-pan   

  1. Department of Mathematics, East China Normal University, Shanghai  200241, China
  • Received:2013-08-01 Revised:2013-10-01 Online:2013-11-25 Published:2014-01-13

PDF

1963

摘要： 设~$\mathscr{F}$~是特征~0~的域,
$q\in\mathscr F$~是个单位根.
以~$\mathscr{F}$~为基域、以~$q$~为量子参数,
令~$\mathsf{s}_q(n)$~为秩~$n$~的限制量子对称代数,
$\Wedge_q(n)$~为秩~$n$~的量子外代数. 据~[6],
$\mathsf{s}_q(n)$~与~$\Wedge_q(n)$~的齐次分量都是单的~$U_q(\mathfrak{gl}_n)$-模.
本文将把~$\mathsf{s}_q(n)$~的齐次分量与~$\Wedge_q(n)$~的齐次分量的张量积分解成不可分解模的直和.

关键词: 量子群, 限制量子对称代数, 量子外代数, Krull--Schmidt\,分解

Abstract: Assume $\mathscr{F}$ to be a field of characteristic zero,
and $q\in \mathscr{F}$ to be a root of unity. With $\mathscr F$ as
the ground field and $q$ as the quantum parameter, let
$\mathsf{s}_q(n)$ be the restricted quantum symmetric algebra of
rank $n$, and $\Wedge_q(n)$ be the quantum exterior algebra of rank
$n$. By [6], the homogenous components of both $\mathsf{s}_q(n)$ and
$\Wedge_q(n)$ are simple $U_q(\mathfrak{gl}_n)$-modules. In this
paper, we decompose the tensor product of any homogenous component
of $\mathsf{s}_q(n)$ with any homogenous component of $\Wedge_q(n)$
into direct sum of indecomposable modules.

Key words: quantum group, restricted quantum symmetric algebra, quantum exterior algebra, Krull--Schmidt decomposition

中图分类号: