RESEARCH ARTICLE

Nil-Coxeter algebras and nil-Ariki-Koike algebras

  • Guiyu YANG
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  • School of Science, Shandong University of Technology, Zibo 255049, China

Received date: 11 May 2014

Accepted date: 28 Aug 2015

Published date: 12 Oct 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

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. Soc, 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 nil-Ariki-Koike algebras.

Cite this article

Guiyu YANG . Nil-Coxeter algebras and nil-Ariki-Koike algebras[J]. Frontiers of Mathematics in China, 2015 , 10(6) : 1473 -1481 . DOI: 10.1007/s11464-015-0498-3

1
Ariki S. Hecke algebras of classical type and their representation type. Proc Lond Math Soc, 2005, 91: 355−413

DOI

2
Ariki S, Koike K. A Hecke algebra of (ℤ/rℤ) ≀Sn and construction of its irreducible representations. Adv Math, 1994, 106: 216−243

3
Bernstein J N, Gelfand I M, Gelfand S I. Schubert cells and cohomology of the spaces G/P. Russian Math Surveys, 1973, 28: 1−26

DOI

4
Brichard J. The center of the Nilcoxeter and 0-Hecke algebras. arXiv: 0811.2590

5
Crawley-Boevey W. Tameness of biserial algebras. Arch Math, 1995, 65: 399−407

DOI

6
Drozd J A. Tame and wild matrix problems. In: Dlab V, Gabriel P, eds. Representation Theory II. Lecture Notes in Math, Vol 832. Berlin-Heidelberg-New York: Springer, 1980, 242−258

DOI

7
Du J, Rui H. Based algebras and standard bases for quasi-hereditary algebras. Trans Amer Math Soc, 1998, 350: 3207−3235

DOI

8
Erdmann K. Blocks of Tame Representation Type and Related Algebras. Lecture Notes in Math, Vol 1428. Berlin: Springer-Verlag, 1990

9
Fomin S, Stanley R P. Schubert polynomials and the nilCoxeter algebra. Adv Math, 1994, 103: 196−207

DOI

10
Graham J, Lehrer G. Cellular algebras. Invent Math, 1996, 123: 1−34

DOI

11
Grojnowski I, Vazirani M. Strong multiplicity one theorems for affine Hecke algebras of type A. Transform Groups, 2001, 6: 143−155

DOI

12
Khovanov M. Nilcoxeter algebras categorify the Weyl algebra. Comm Algebra, 2001, 29: 5033−5052

DOI

13
Khovanov M, Lauda A D. A diagrammatic approach to categorification of quantum groups I. Represent Theory, 2009, 13: 309−347

DOI

14
Lenzing H. Invariance of tameness under stable equivalence: Krause’s theorem. In: Krause H, Ringel C M, eds. Infinite Length Modules. Trends in Mathematics. Boston: Birkhäuser, 2000, 405−418

DOI

15
Rouquier R. Quiver Hecke algebras and 2-Lie algebras. Algebra Colloq, 2012, 19: 359−410

DOI

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