Nil-Coxeter algebras and nil-Ariki-Koike algebras  

作　　者：Guiyu YANG 

机构地区：[1]School of Science, Shandong University of Technology, Zibo 255049, China

出　　处：《Frontiers of Mathematics in China》2015年第6期1473-1481,共9页中国高等学校学术文摘·数学（英文）

基　　金：Acknowledgements The author was grateful to the referees for their detailed reading and helpful suggestions. This work was supported by the National Natural Science Foundation of China （Grant No. 11201269）, the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, and the Young Scholars Research Fund of Shandong University of Technology.

摘　　要：We investigate the properties of nil-Coxeter algebras and nil-Ariki- Koike algebras. To be precise, from the view of standardly based algebras introduced by J. Du, H. Rui [Trans. Amer. Math. Soe, 1998, 350： 3207-3235], we give a description of simple modules of nil-Coxeter algebras and nil-Ariki-Koike algebras. Then we determine the representation type of nil-Coxeter algebras and nil-Ariki-Koike algebras. We also give a description of the center of nilAriki-Koike algebras.We investigate the properties of nil-Coxeter algebras and nil-Ariki- Koike algebras. To be precise, from the view of standardly based algebras introduced by J. Du, H. Rui [Trans. Amer. Math. Soe, 1998, 350： 3207-3235], we give a description of simple modules of nil-Coxeter algebras and nil-Ariki-Koike algebras. Then we determine the representation type of nil-Coxeter algebras and nil-Ariki-Koike algebras. We also give a description of the center of nilAriki-Koike algebras.

关 键 词：nil-Coxeter algebras nil-Ariki-Koike algebras 

分 类 号：O1[理学—数学]