Grobner-Shirshov pair of irreducible modules over quantized enveloping algebra of type A(n)

Tunyaz Rabigul; Obul Abdukadir

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Grobner-Shirshov pair of irreducible modules over quantized enveloping algebra of type A(n)

机译：Grobner-shirshov对IDS（n）型的量化包络代数

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摘要

In this paper, first, we give a Grobner-Shirshov pair of finite-dimensional irreducible module V-q(lambda) over U-q(A(n)), the quantized enveloping algebra of type An, by using the double free module method and the known Grobner-Shirshov basis of U-q(A(n)). Then, by specializing a suitable version of U-q(A(n)) at q = 1, we get a Grobner-Shirshov basis of U(A(n)), and get a Grobner-Shirshov pair for the finite-dimensional irreducible module V (lambda) over U(A(n)).

机译：本文首先利用二次自由模方法和已知的U-q（a（n））的Grobner-Shirshov基，给出了n型量子化包络代数U-q（a（n））上有限维不可约模V-q（lambda）的Grobner-Shirshov对。然后，通过在q=1时专门化U-q（a（n））的一个合适版本，我们得到了U（a（n））的Grobner-Shirshov基，并得到了U（a（n））上有限维不可约模V（lambda）的Grobner-Shirshov对。

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来源
《Journal of algebra and its applications》 |2018年第2期|共16页
作者
Tunyaz Rabigul; Obul Abdukadir;
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作者单位

Xinjiang Univ Coll Math &

Syst Sci Urumqi 830046 Xinjiang Peoples R China;

Xinjiang Univ Coll Math &

Syst Sci Urumqi 830046 Xinjiang Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类代数、数论、组合理论;
关键词
Quantized enveloping algebra; Grobner-Shirshov basis; double free module; indecomposable module; highest weight module;

机译：量化包络代数;Grobner-Shirshov基础;双自由模块;不可分离的模块;最高重量模块;

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1. Categorification of Spin Modules of Enveloping Algebra of Lie Algebra of Type D_4 [J] . Huabo XU, Shilin YANG 数学研究及应用：英文版 . 2014,第006期
2. Grobner-Shirshov pair of irreducible modules over quantized enveloping algebra of type A(n) [J] . Tunyaz Rabigul, Obul Abdukadir Journal of algebra and its applications . 2018,第2期

机译：Grobner-shirshov对IDS（n）型的量化包络代数
3. Computing with Quantized enveloping Algebras: PBW-Type Bases, Highest-Weight Modules and R-Matrices [J] . W. A. De Graaf urnal of Symbolic Computation . 2001,第5期

机译：使用量化包络代数进行计算：PBW型基数，最高权重模块和R矩阵
4. q-wedge modules for quantized enveloping algebras of classical type [J] . Jing NH., Okado M., Misra KC. Journal of Algebra . 2000,第2期

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5. Grobner-shirshov bases for repressentations of lie algebras and hecke algebras of type A [C] . Kyu-Hwan Lee International Conference on Algebra and Their Related Topics . 2003

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6. A Skein-theoretic construction of invariants of 3-manifolds associated to the quantized universal enveloping algebra for a simple Lie algebra. [D] . O'Brien, Timothy John. 2002

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7. IRREDUCIBLE OPERATOR ALGEBRAS [O] . Richard V. Kadison 1957

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8. Irreducible Modules of Quantized Enveloping Algebras at Roots of 1, II [O] . Nanhua Xi 1996

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9. Characters of the Irreducible Highest Weight Modules over the Virasoro and Super-Virasoro Algebras [R] . 1986

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Grobner-Shirshov pair of irreducible modules over quantized enveloping algebra of type A(n)

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