全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

单位根处的某些单Uq(gln)}-模的Krull--Schmidt分解

, PP. 1-13

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

Full-Text   Cite this paper   Add to My Lib

Abstract:

设~$\mathscr{F}$~是特征~0~的域,$q\in\mathscrF$~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.

References

[1]  AW} ANDERSEN H H, WEN K X. Representations of quantum algebras, the mixed case [J]. Journal f\"ur die Reine und Angewandte Mathematik, 1992, 427: 35--50.
[2]  COX A. The blocks of the q-Schur algebra [J]. Journal of Algebra, 1998, 207: 306--325.
[3]  CHARI V, PREMET A. Indecomposable restricted representations of quantum \mathfrak{sl}_2 [J]. Publications RIMS Kyoto University, 1994, 30: 335--352.
[4]  DENG B M, DU J, PARSHALL B, WANG J P. Finite Dimensional Algebras and Quantum Groups [M]. Mathematical Surveys and Monographs, Volume 150. Providence R I: American Mathematical Society, 2008.
[5]  DU J, FU Q, WANG J P. Infinitesimal quantum \mathfrak{gl}_n and little q-Schur algebras [J]. Journal of Algebra, 2005, 287: 199--233.
[6]  HU N H. Quantum divided power algebra, q-derivatives, some new quantum groups [J]. Journal of Algebra, 2000, 232: 507--540.
[7]  JANTZEN J C. Lectures on Quantum Groups [M]. Graduate Studies in Mathematics, Volume 6. Providence R I: American Mathematical Society, 1996.
[8]  KONDO H, SAITO Y. Indecomposable decomposition of tensor products of modules over the restricted quantum universal enveloping algebra
[9]  associated to \mathfrak{sl}_2 [EB/OL]. arXiv: 0901. 4221v2 [math. AQ], 2009.
[10]  LUSZTIG G. Finite dimensional Hopf algebras arising from quantized universal enveloping algebras [J]. Journal of the American Mathematical Society, 1990, 3: 447--498.
[11]  LUSZTIG G. Introduction to Quantum Groups [M]. Progress in Mathematics, Volume 110. Boston: Birkh\"auser, 1993.
[12]  MANIN Yu I. Quantum Groups and Non-Commutative Geometry [M]. Montr\''eal: CRM, Universite de Montr\''eal, 1988.
[13]  PARSHALL B, WANG J P. Quantum Linear Groups [M]. Memoirs American Mathematical Society, No.~439. Providence R I: American Mathematical Society, 1991.
[14]  XIAO J. Finite dimensional representations of \overline{U_t(\mathfrak{sl}_2)} at roots of unity [J]. Canadian Journal of Mathematics, 1997, 49: 772--787.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133