Acta mathematica scientia, Series B >
THE CANONICAL BASIS FOR THE QUANTUM GROUP OF TYPE B2
Received date: 2010-10-25
Revised date: 2012-12-05
Online published: 2013-09-20
We use the Ringel-Hall algebra approach to study the canonical basis elements for the quantum group of type B2 which are characterized in Xi [12]. However, our approach simplifies several computations there.
Key words： Ringel-Hall algebras; representations; quantum groups; Canonical basis
ZHANG Jie . THE CANONICAL BASIS FOR THE QUANTUM GROUP OF TYPE B2[J]. Acta mathematica scientia, Series B, 2013 , 33(5) : 1499 -1506 . DOI: 10.1016/S0252-9602(13)60099-5
[1] Auslander M, Reiten I, Smal S O. Representation Theory of Artin Algebras. Cambridge Studies
i n Advanced Mathematics 36. Cambridge: Cambridge University Press, 1995
[2] Deng B M, Du J. Monomial Bases for quantum affine sln. Adv Math, 2005, 191: 276–304
[3] Deng B M, Du J. On bases of quantized enveloping algebras. Pacific J Math, 2005, 202: 33–48
[4] Deng B M, Du J, Parshall B, Wang J P. Finite Dimensional Algebras and Quantum Groups. Mathematical Surveys and Monographs 150. Providence RI: Amer Math Soc, 2008
[5] Dlab V. and Ringel C M. Indecomposable Representations of Graphs and Algebras. Memoirs Amer Math Soc 173. Providence RI: Amer Math Soc, 1976
[6] Lusztig G. Canonical bases arising from quantized enveloping algebras. J Amer Math Soc, 1990, 3: 447–498
[7] Lusztig G. Introduction to Quantum Groups. Progress in Mathematics, Vol 110. Boston, Basel, Berlin: Birkhauser, 1993
[8] Ringel C M. Hall algebras//Topics in Algebra, 66. Banach Center Publications, 1990: 433–447
[9] Ringel C M. Hall algebras and quantum groups. Invent Math, 1990, 101: 583–592
[10] Ringel C M. The Hall algebra approach to quantum groups. Aportaciones Matem´aticas Comunicaciones, 1995, 15: 85–114
[11] Ringel C M. PBW-bases of quantum groups. J Reine Angew Math, 1996, 470: 51–88
[12] Xi N H. Canonical basis for type B2. J Algebra, 1999, 214: 8–21
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