A型退化仿射Hecke代数的Grbner-Shirshov基
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摘要
给出了A型退化仿射Hecke代数的Grbner-Shirshov基,并且用此Grbner-Shirshov基和结合代数的钻石合成引理,给出A型退化仿射Hecke代数的一组线性基。
A Grbner-Shirshov basis of degenerate affine Hecke algebra of type A is given. By using this Grbner-Shirshov basis and the composition-diamond lemma of associative algebras,a linear basis of the degenerate affine Hecke algebra of type A is constructed.
A Grbner-Shirshov basis of degenerate affine Hecke algebra of type A is given. By using this Grbner-Shirshov basis and the composition-diamond lemma of associative algebras,a linear basis of the degenerate affine Hecke algebra of type A is constructed.
引文
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[2]BERGMAN G M. The diamond lemma for ring theory[J]. Adv in Math,1978,29:178-218.
[3]SHIRSHOV A I. Some algorithmic problem for Lie algebras[J]. Sibirsk Mat Z,1962,3(2):292-296.
[4]BOKUT L A. Embeddings into simple associative algebras[J]. Algebra and Logic,1976,15(2):73-90.
[5]高珍珍,杨士林,阿布都卡的·吾甫.Anick分解和量子群Uq(sl2)的一些同调性质[J].山东大学学报(理学版),2014,49(10):17-27.GAO Zhenzhen,YANG Shilin,Abdukadir Obul. Anick resolution and some homological properties of quantum group Uq(sl2)[J]. Journal of Shandong University(Natural Science),2014,49(10):17-27.
[6]热比古丽·吐尼亚牧,阿布都卡的·吾甫.量子包络代数Uq(An)的Gelfand-Krillov维数[J].山东大学学报(理学版)2017,52(10):12-23.Tuniyazi Rebiguli,Abdukadir Obul. Gelfand-Krillov dimension of quantum enveloping algebra Uq(An)[J]. Journal of Shan-dong University(Natural Science),2017,52(10):12-23.
[7]MACDONALD I G. Affine Hecke algebras and orthogonal polynomials[M]//Cambridge Tacts in Mathematics. Cambridge:Cambridge University Press,2003,157.
[8]BOKUT L A,CHEN Y Q. Grbner-Shirshov bases:some new results[M]//Proceedings of the Second International Congressin Algebra and Combinatorics. New York:World Scientific,2008:35-56.
[9]HU J,LI F. On the modified affine Hecke algebras and quiver Hecke algebras of type A[EB/OL].(2016-08-18)[2018-08-11]. http://cn.arxiv.org/abs/1608.05453. arxiv:1608.0545v3
[2]BERGMAN G M. The diamond lemma for ring theory[J]. Adv in Math,1978,29:178-218.
[3]SHIRSHOV A I. Some algorithmic problem for Lie algebras[J]. Sibirsk Mat Z,1962,3(2):292-296.
[4]BOKUT L A. Embeddings into simple associative algebras[J]. Algebra and Logic,1976,15(2):73-90.
[5]高珍珍,杨士林,阿布都卡的·吾甫.Anick分解和量子群Uq(sl2)的一些同调性质[J].山东大学学报(理学版),2014,49(10):17-27.GAO Zhenzhen,YANG Shilin,Abdukadir Obul. Anick resolution and some homological properties of quantum group Uq(sl2)[J]. Journal of Shandong University(Natural Science),2014,49(10):17-27.
[6]热比古丽·吐尼亚牧,阿布都卡的·吾甫.量子包络代数Uq(An)的Gelfand-Krillov维数[J].山东大学学报(理学版)2017,52(10):12-23.Tuniyazi Rebiguli,Abdukadir Obul. Gelfand-Krillov dimension of quantum enveloping algebra Uq(An)[J]. Journal of Shan-dong University(Natural Science),2017,52(10):12-23.
[7]MACDONALD I G. Affine Hecke algebras and orthogonal polynomials[M]//Cambridge Tacts in Mathematics. Cambridge:Cambridge University Press,2003,157.
[8]BOKUT L A,CHEN Y Q. Grbner-Shirshov bases:some new results[M]//Proceedings of the Second International Congressin Algebra and Combinatorics. New York:World Scientific,2008:35-56.
[9]HU J,LI F. On the modified affine Hecke algebras and quiver Hecke algebras of type A[EB/OL].(2016-08-18)[2018-08-11]. http://cn.arxiv.org/abs/1608.05453. arxiv:1608.0545v3