메뉴 건너뛰기




Volumn 51, Issue 6, 1999, Pages 1307-1336

Quadratic integers and coxeter groups

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0033273038     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-1999-060-6     Document Type: Article
Times cited : (9)

References (42)
  • 2
    • 0039952933 scopus 로고
    • Geometrische darstellung der gruppen linearer substitutionen mit ganzen complexen coefficienten nebst anwendungen auf die zahlentheorie
    • L. Bianchi, Geometrische Darstellung der Gruppen linearer Substitutionen mit ganzen complexen Coefficienten nebst Anwendungen auf die Zahlentheorie. Math. Ann. 38(1891), 313-333; reprinted in Opere vol. I, pt. 1 (Edizione Cremonese, Rome, 1952), 233-258.
    • (1891) Math. Ann. , vol.38 , pp. 313-333
    • Bianchi, L.1
  • 3
    • 0039952933 scopus 로고
    • reprinted, Edizione Cremonese, Rome
    • L. Bianchi, Geometrische Darstellung der Gruppen linearer Substitutionen mit ganzen complexen Coefficienten nebst Anwendungen auf die Zahlentheorie. Math. Ann. 38(1891), 313-333; reprinted in Opere vol. I, pt. 1 (Edizione Cremonese, Rome, 1952), 233-258.
    • (1952) Opere , vol.1 , Issue.PT. 1 , pp. 233-258
  • 4
    • 0000762274 scopus 로고
    • Sui gruppi de sostituzioni lineari con coeficienti appartenenti a corpi quadratici imaginari
    • _, Sui gruppi de sostituzioni lineari con coeficienti appartenenti a corpi quadratici imaginari. Math. Ann. 40(1892), 332-412; reprinted in Opere vol. I, pt. 1 (Edizione Cremonese, Rome, 1952), 270-373.
    • (1892) Math. Ann. , vol.40 , pp. 332-412
  • 5
    • 0000762274 scopus 로고
    • reprinted, Edizione Cremonese, Rome
    • _, Sui gruppi de sostituzioni lineari con coeficienti appartenenti a corpi quadratici imaginari. Math. Ann. 40(1892), 332-412; reprinted in Opere vol. I, pt. 1 (Edizione Cremonese, Rome, 1952), 270-373.
    • (1952) Opere , vol.1 , Issue.PT. 1 , pp. 270-373
  • 6
    • 0000243546 scopus 로고
    • Discrete groups generated by reflections
    • H. S. M. Coxeter, Discrete groups generated by reflections. Annals of Math. (2) 35(1934), 588-621; reprinted in Kaleidoscopes: Selected Writings of H. S. M. Coxeter (eds. F. A. Sherk, P. McMullen, A. C. Thompson, A. I. Weiss), Wiley, New York, 1995, 145-178.
    • (1934) Annals of Math. (2) , vol.35 , pp. 588-621
    • Coxeter, H.S.M.1
  • 7
    • 0039952934 scopus 로고
    • reprinted (eds. F. A. Sherk, P. McMullen, A. C. Thompson, A. I. Weiss), Wiley, New York
    • H. S. M. Coxeter, Discrete groups generated by reflections. Annals of Math. (2) 35(1934), 588-621; reprinted in Kaleidoscopes: Selected Writings of H. S. M. Coxeter (eds. F. A. Sherk, P. McMullen, A. C. Thompson, A. I. Weiss), Wiley, New York, 1995, 145-178.
    • (1995) Kaleidoscopes: Selected Writings of H. S. M. Coxeter , pp. 145-178
  • 8
    • 0000161496 scopus 로고
    • Regular honeycombs in hyperbolic space
    • Amsterdam, Noordhoff, Groningen, and North-Holland, Amsterdam
    • _, Regular honeycombs in hyperbolic space. Proc. Internat. Congress of Mathematicians (Amsterdam, 1954), Vol. III, Noordhoff, Groningen, and North-Holland, Amsterdam, 1956, 155-169; reprinted in Twelve Geometric Essays, Southern Illinois Univ. Press, Carbondale, IL, and Feffer & Simons, London-Amsterdam, 1968, 199-214.
    • (1954) Proc. Internat. Congress of Mathematicians , vol.3 , pp. 155-169
  • 9
    • 0004138036 scopus 로고
    • reprinted, Southern Illinois Univ. Press, Carbondale, IL, and Feffer & Simons, London-Amsterdam
    • _, Regular honeycombs in hyperbolic space. Proc. Internat. Congress of Mathematicians (Amsterdam, 1954), Vol. III, Noordhoff, Groningen, and North-Holland, Amsterdam, 1956, 155-169; reprinted in Twelve Geometric Essays, Southern Illinois Univ. Press, Carbondale, IL, and Feffer & Simons, London-Amsterdam, 1968, 199-214.
    • (1968) Twelve Geometric Essays , pp. 199-214
  • 10
    • 0009919307 scopus 로고
    • Generators and relations for discrete groups
    • Springer-Verlag, Berlin-Göttingen-Heidelberg
    • H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups. Ergeb. Math. Grenzgeb. (N.F.), Bd. 14, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957; 4th edn, idem, Berlin-Heidelberg-New York, 1980.
    • (1957) Ergeb. Math. Grenzgeb. (N.F.) , vol.14
    • Coxeter, H.S.M.1    Moser, W.O.J.2
  • 11
    • 85033973528 scopus 로고
    • Berlin-Heidelberg-New York
    • H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups. Ergeb. Math. Grenzgeb. (N.F.), Bd. 14, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957; 4th edn, idem, Berlin-Heidelberg-New York, 1980.
    • (1980) 4th Edn, Ergeb. Math. Grenzgeb. (N.F.)
  • 13
    • 0011373487 scopus 로고
    • Algebraic theory of the Bianchi groups
    • Marcel Dekker, New York-Basel
    • B. Fine, Algebraic Theory of the Bianchi Groups. Pure Appl. Math. 129, Marcel Dekker, New York-Basel, 1989.
    • (1989) Pure Appl. Math. , vol.129
    • Fine, B.1
  • 14
    • 84967780443 scopus 로고
    • The normal subgroup structure of the Picard group
    • B. Fine and M. Newman, The normal subgroup structure of the Picard group. Trans. Amer. Math. Soc. 302(1987), 769-786.
    • (1987) Trans. Amer. Math. Soc. , vol.302 , pp. 769-786
    • Fine, B.1    Newman, M.2
  • 18
    • 0004133524 scopus 로고
    • Springer-Verlag, Berlin-Heidelberg-New York, translated by P. Shiu from the 1957 Chinese original
    • L. K. Hua, Introduction to Number Theory. Springer-Verlag, Berlin-Heidelberg-New York, 1982 (translated by P. Shiu from the 1957 Chinese original).
    • (1982) Introduction to Number Theory
    • Hua, L.K.1
  • 20
    • 0041139905 scopus 로고
    • Absolute polarities and central inversions
    • (eds. C. Davis, B. Grunbaum and F. A. Sherk), Springer-Verlag, New York-Heidelberg-Berlin
    • N. W. Johnson, Absolute polarities and central inversions. In: The Geometric Vein: The Coxeter Festchrift (eds. C. Davis, B. Grunbaum and F. A. Sherk), Springer-Verlag, New York-Heidelberg-Berlin, 1981, 443-464.
    • (1981) The Geometric Vein: The Coxeter Festchrift , pp. 443-464
    • Johnson, N.W.1
  • 22
    • 0041139902 scopus 로고
    • Ueber die transformation der elliptischen functionen und die auflösung der gleichungen fünften grades
    • F. Klein, Ueber die Transformation der elliptischen Functionen und die Auflösung der Gleichungen fünften Grades. Math. Ann. 14(1879), 111-172; reprinted in Gesammelte mathematische Abhandlungen, Bd. III, Springer, Berlin, 1923, 13-75.
    • (1879) Math. Ann. , vol.14 , pp. 111-172
    • Klein, F.1
  • 23
    • 0041139902 scopus 로고
    • reprinted, Springer, Berlin
    • F. Klein, Ueber die Transformation der elliptischen Functionen und die Auflösung der Gleichungen fünften Grades. Math. Ann. 14(1879), 111-172; reprinted in Gesammelte mathematische Abhandlungen, Bd. III, Springer, Berlin, 1923, 13-75.
    • (1923) Gesammelte Mathematische Abhandlungen , vol.3 , pp. 13-75
  • 24
  • 25
    • 0011264364 scopus 로고
    • On complexes with transitive groups of automorphisms
    • F. Lannér, On complexes with transitive groups of automorphisms. Medd. Lunds Univ. Mat. Sem. 11(1950), 1-71.
    • (1950) Medd. Lunds Univ. Mat. Sem. , vol.11 , pp. 1-71
    • Lannér, F.1
  • 26
    • 0003845960 scopus 로고
    • Macmillan, New York, and Collier-Macmillan, London; 3rd edn, Chelsea, New York, 1987
    • S. Mac Lane and G. Birkhoff, Algebra. Macmillan, New York, and Collier-Macmillan, London, 1967; 3rd edn, Chelsea, New York, 1987.
    • (1967) Algebra
    • Mac Lane, S.1    Birkhoff, G.2
  • 29
    • 21844527405 scopus 로고
    • Polytopes related to the Picard group
    • B. Monson and A. I. Weiss, Polytopes related to the Picard group. Linear Algebra Appl. 218(1995), 185-204.
    • (1995) Linear Algebra Appl. , vol.218 , pp. 185-204
    • Monson, B.1    Weiss, A.I.2
  • 30
    • 0010566324 scopus 로고    scopus 로고
    • Eisenstein integers and related C-groups
    • _, Eisenstein integers and related C-groups. Geom. Dedicata 66(1997), 99-117.
    • (1997) Geom. Dedicata , vol.66 , pp. 99-117
  • 33
    • 0011413837 scopus 로고
    • Sur un groupe des transformations des points de l'espace situés du même côté d'un plan
    • É. Picard, Sur un groupe des transformations des points de l'espace situés du même côté d'un plan. Bull. Soc. Math. France 12(1884), 43-47, reprinted in Œuvres, t. I (Centre National de la Recherche Scientifique, Paris, 1978), 499-504.
    • (1884) Bull. Soc. Math. France , vol.12 , pp. 43-47
    • Picard, É.1
  • 34
    • 85033950139 scopus 로고
    • reprinted, Centre National de la Recherche Scientifique, Paris
    • É. Picard, Sur un groupe des transformations des points de l'espace situés du même côté d'un plan. Bull. Soc. Math. France 12(1884), 43-47, reprinted in Œuvres, t. I (Centre National de la Recherche Scientifique, Paris, 1978), 499-504.
    • (1978) Œuvres , vol.1 , pp. 499-504
  • 35
    • 0003274790 scopus 로고
    • Foundations of hyperbolic manifolds
    • Springer-Verlag, New York-Berlin-Heidelberg
    • J. G. Ratcliffe, Foundations of Hyperbolic Manifolds. Graduate Texts in Math. 149, Springer-Verlag, New York-Berlin-Heidelberg, 1994.
    • (1994) Graduate Texts in Math. , vol.149
    • Ratcliffe, J.G.1
  • 37
    • 0001748288 scopus 로고
    • Chirality and projective linear groups
    • E. Schulte and A. I. Weiss, Chirality and projective linear groups. Discrete Math. 131(1994), 221-261.
    • (1994) Discrete Math. , vol.131 , pp. 221-261
    • Schulte, E.1    Weiss, A.I.2
  • 38
    • 0004256857 scopus 로고
    • Ginn, Boston
    • O. Veblen and J. W. Young, Projective Geometry, Vol. I. Ginn, Boston, 1910; idem, 1916; Blaisdell, New York-Toronto-London, 1965.
    • (1910) Projective Geometry , vol.1
    • Veblen, O.1    Young, J.W.2
  • 39
    • 0004256857 scopus 로고
    • O. Veblen and J. W. Young, Projective Geometry, Vol. I. Ginn, Boston, 1910; idem, 1916; Blaisdell, New York-Toronto-London, 1965.
    • (1916) Projective Geometry
  • 40
    • 0004256857 scopus 로고
    • Blaisdell, New York-Toronto-London
    • O. Veblen and J. W. Young, Projective Geometry, Vol. I. Ginn, Boston, 1910; idem, 1916; Blaisdell, New York-Toronto-London, 1965.
    • (1965) Projective Geometry
  • 41
    • 0004256857 scopus 로고
    • Ginn, Boston
    • _, Projective Geometry, Vol. II. Ginn, Boston, 1918; Blaisdell, New York-Toronto-London, 1965.
    • (1918) Projective Geometry , vol.2
  • 42
    • 0004256857 scopus 로고
    • Blaisdell, New York-Toronto-London
    • _, Projective Geometry, Vol. II. Ginn, Boston, 1918; Blaisdell, New York-Toronto-London, 1965.
    • (1965) Projective Geometry


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.