메뉴 건너뛰기




Volumn 7, Issue 1, 2001, Pages 1-56

Affine Lie algebras and tame quivers

Author keywords

Affine lie algebra; Hall algebra; Tame quiver

Indexed keywords


EID: 1542539308     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/PL00001397     Document Type: Article
Times cited : (14)

References (26)
  • 1
  • 2
    • 85037312739 scopus 로고    scopus 로고
    • Bou68 Fase. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Hermann, Paris, 1968, Actualités Scientifiques et Industrielles
    • [Bou68] N. Bourbaki. Éléments de mathématique. Fase. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Hermann, Paris, 1968, Actualités Scientifiques et Industrielles, No. 1337.
    • Éléments De Mathématique , Issue.1337
    • Bourbaki, N.1
  • 5
    • 0003094115 scopus 로고
    • Indecomposable representations of graphs and algebras
    • DR76
    • [DR76] V. Dlab and C. M. Ringel. Indecomposable representations of graphs and algebras. Mem. Amer. Math. Soc. 6 (1976), v+57.
    • (1976) Mem. Amer. Math. Soc. , vol.6 , pp. 57
    • Dlab, V.1    Ringel, C.M.2
  • 6
    • 0002630015 scopus 로고
    • Basic representations of affine Lie algebras and dual resonance models
    • FK80
    • [FK80] I. B. Frenkel and V. G. Kac. Basic representations of affine Lie algebras and dual resonance models. Invent. Math. 62 (1980), 23-66.
    • (1980) Invent. Math. , vol.62 , pp. 23-66
    • Frenkel, I.B.1    Kac, V.G.2
  • 7
    • 0000814037 scopus 로고
    • Representations of Kac-Moody algebras and dual resonance models. Applications of group theory in physics and mathematical physics (Chicago, 1982)
    • Fre85 Providence, R.I.
    • [Fre85] I. B. Frenkel. Representations of Kac-Moody algebras and dual resonance models. Applications of group theory in physics and mathematical physics (Chicago, 1982), Amer. Math. Soc., Providence, R.I., 1985, 325-353.
    • (1985) Amer. Math. Soc. , pp. 325-353
    • Frenkel, I.B.1
  • 8
    • 0003025155 scopus 로고
    • Unzerlegbare Darstellungen
    • Gab72 correction, ibid 6 (1972), 309
    • [Gab72] P. Gabriel. Unzerlegbare Darstellungen. I. Manuscripta Math 6 (1972), 71-103; correction, ibid 6 (1972), 309.
    • (1972) I. Manuscripta Math , vol.6 , pp. 71-103
    • Gabriel, P.1
  • 10
    • 0040686489 scopus 로고
    • Algebraische reduction der schaaren bilinearer formen
    • Kro90
    • [Kro90] L. Kronecker. Algebraische reduction der schaaren bilinearer formen. Sitzungsberichte Akad. Berlin 1890 (1890), 1225-1237.
    • (1890) Sitzungsberichte Akad. Berlin , vol.1890 , pp. 1225-1237
    • Kronecker, L.1
  • 11
    • 84968494076 scopus 로고
    • Quivers, perverse sheaves, and quantized enveloping algebras
    • Lus91a
    • [Lus91a] G. Lusztig. Quivers, perverse sheaves, and quantized enveloping algebras. J. Amer. Math. Soc. 4 (1991), 365-421.
    • (1991) J. Amer. Math. Soc. , vol.4 , pp. 365-421
    • Lusztig, G.1
  • 12
    • 0010988073 scopus 로고
    • Intersection cohomology methods in representation theory
    • Lus91b (Kyoto, 1990) (Tokyo). Math. Soc. Japan
    • [Lus91b] G. Lusztig. Intersection cohomology methods in representation theory. Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990) (Tokyo). Math. Soc. Japan, 1991, 155-174.
    • (1991) Proceedings of the International Congress of Mathematicians , vol.1-2 , pp. 155-174
    • Lusztig, G.1
  • 13
  • 14
    • 0000777958 scopus 로고
    • Chern classes for singular algebraic varieties
    • Mac74
    • [Mac74] R. D. MacPherson. Chern classes for singular algebraic varieties. Ann. of Math. (2) 100 (1974), 423-432.
    • (1974) Ann. of Math. (2) , vol.100 , pp. 423-432
    • MacPherson, R.D.1
  • 15
    • 0001280810 scopus 로고
    • Graphs, singularities, and finite groups
    • McK80 The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979), Providence, R.I.
    • [McK80] J. McKay. Graphs, singularities, and finite groups. The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979), Amer. Math. Soc., Providence, R.I., 1980, 183-186.
    • (1980) Amer. Math. Soc. , pp. 183-186
    • McKay, J.1
  • 16
    • 0001473466 scopus 로고
    • Toroidal Lie algebras and vertex representations
    • MRY90
    • [MRY90] R. V. Moody, S. E. Rao, and T. Yokonuma. Toroidal Lie algebras and vertex representations. Geom. Dedicate 35 (1990), 283-307.
    • (1990) Geom. Dedicate , vol.35 , pp. 283-307
    • Moody, R.V.1    Rao, S.E.2    Yokonuma, T.3
  • 17
    • 0000866141 scopus 로고
    • Representations of quivers of infinite type
    • Naz73
    • [Naz73] L. A. Nazarova. Representations of quivers of infinite type. Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973), 752-791.
    • (1973) Izv. Akad. Nauk SSSR Ser. Mat. , vol.37 , pp. 752-791
    • Nazarova, L.A.1
  • 18
    • 0031537307 scopus 로고    scopus 로고
    • Root categories and simple Lie algebras
    • PX97
    • [PX97] L. Peng and J. Xiao. Root categories and simple Lie algebras. J. Algebra 198 (1997), 19-56.
    • (1997) J. Algebra , vol.198 , pp. 19-56
    • Peng, L.1    Xiao, J.2
  • 19
    • 0001452593 scopus 로고
    • Lie algebras generated by indecomposables
    • Rie94
    • [Rie94] Ch. Riedtmann. Lie algebras generated by indecomposables. J. Algebra 170 (1994), 526-546.
    • (1994) J. Algebra , vol.170 , pp. 526-546
    • Riedtmann, Ch.1
  • 21
    • 52549119672 scopus 로고
    • Rin90b Topics in algebra, Part 1 (Warsaw, 1988). PWN, Warsaw
    • [Rin90b] C. M. Ringel. Hall algebras. Topics in algebra, Part 1 (Warsaw, 1988). PWN, Warsaw, 1990, 433-447.
    • (1990) Hall Algebras , pp. 433-447
    • Ringel, C.M.1
  • 22
    • 0001164614 scopus 로고
    • Hall polynomials for the representation-finite hereditary algebras
    • Rin90c
    • [Rin90c] C. M. Ringel. Hall polynomials for the representation-finite hereditary algebras. Adv. Math. 84 (1990), 137-178.
    • (1990) Adv. Math. , vol.84 , pp. 137-178
    • Ringel, C.M.1
  • 23
    • 84963002139 scopus 로고
    • The composition algebra of a cyclic quiver. Towards an explicit description of the quantum group of type
    • Rin93
    • n. Proc. London Math. Soc. (3) 66 (1993), 507-537.
    • (1993) n. Proc. London Math. Soc. (3) , vol.66 , pp. 507-537
    • Ringel, C.M.1
  • 25
    • 33744722285 scopus 로고
    • Unitary representations of some infinite-dimensional groups
    • Seg81
    • [Seg81] G. Segal. Unitary representations of some infinite-dimensional groups. Comm. Math. Phys. 80 (1981), 301-342.
    • (1981) Comm. Math. Phys. , vol.80 , pp. 301-342
    • Segal, G.1
  • 26
    • 84972567361 scopus 로고
    • 2, Dynkin diagrams and affine Coxeter elements
    • Ste85
    • 2, Dynkin diagrams and affine Coxeter elements. Pacific J. Math. 118 (1985), 587-598.
    • (1985) Pacific J. Math. , vol.118 , pp. 587-598
    • Steinberg, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.