On Vassiliev invariants not coming from semisimple Lie algebras

被引：6
|
作者：
Lieberum, J [1 ]
机构：
[1] Univ Strasbourg 1, CNRS, Inst Rech Math Avancee, F-67084 Strasbourg, France
来源：
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 1999年 / 8卷 / 05期
关键词：
knots; Vassiliev invariants; Lie superalgebras;
D O I：
10.1142/S0218216599000420
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove a refinement of Vogel's statement that the Vassiliev invariants of knots coming from semisimple Lie algebras do not generate all Vassiliev invariants. This refinement takes into account the second grading on the Vassiliev invariants induced by cabling of knots. As an application we get an amelioration of the actually known lower bounds for the dimensions of the space of Vassiliev invariants.
引用
收藏
页码：659 / 666
页数：8
相关论文
共 50 条
  • [41] On differential invariants of actions of semisimple Lie groups
    Bibikov, Pavel
    Lychagin, Valentin
    JOURNAL OF GEOMETRY AND PHYSICS, 2014, 85 : 99 - 105
  • [42] THE SEMISIMPLE SUBALGEBRAS OF LIE-ALGEBRAS
    FELDMAN, G
    FULTON, T
    MATTHEWS, PT
    JOURNAL OF MATHEMATICAL PHYSICS, 1984, 25 (05) : 1230 - 1252
  • [43] Filtrations in semisimple lie algebras, II
    Barnea, Y.
    Passman, D. S.
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (02) : 801 - 817
  • [44] Decomposition varieties in semisimple Lie algebras
    Broer, A
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1998, 50 (05): : 929 - 971
  • [45] REPRESENTATIONS OF COMPLEX SEMISIMPLE LIE GROUPS AND LIE ALGEBRAS
    PARTHASA.KR
    RAO, RR
    VARADARA.VS
    BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 72 (03) : 522 - &
  • [46] An evaluation on Real Semisimple Lie Algebras
    MENG DaojiDepartment of Mathematics
    ChineseScienceBulletin, 2000, (09) : 861 - 864
  • [47] Integrable triples in semisimple Lie algebras
    De Sole, Alberto
    Jibladze, Mamuka
    Kac, Victor G.
    Valeri, Daniele
    LETTERS IN MATHEMATICAL PHYSICS, 2021, 111 (05)
  • [48] SEMISIMPLE GRADED LIE-ALGEBRAS
    PAIS, A
    RITTENBERG, V
    JOURNAL OF MATHEMATICAL PHYSICS, 1975, 16 (10) : 2062 - 2073
  • [49] Cyclic elements in semisimple lie algebras
    Elashvili, A. G.
    Kac, V. G.
    Vinberg, E. B.
    TRANSFORMATION GROUPS, 2013, 18 (01) : 97 - 130
  • [50] GENERATORS OF SEMISIMPLE LIE-ALGEBRAS
    IONESCU, T
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (06): : A568 - A568
12345