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Elliptic Hopf Algebras
Author(s) -
Félix Yves,
Halperin Stephen,
Thomas JeanClaude
Publication year - 1991
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-43.3.545
Subject(s) - hopf algebra , noetherian , mathematics , quasitriangular hopf algebra , pure mathematics , nilpotent , noetherian ring , discrete mathematics , finitely generated abelian group , algebra over a field , division algebra , subalgebra
An elliptic Hopf algebra is a connected graded cocommutative Hopf algebra that is finitely generated and nilpotent. If ( A, m, k ) is a local noetherian ring then Ext A ( k ; k ) is elliptic if and only if A is a complete intersection. Similarly, special conditions are imposed on a simply connected topological space X if H ∗ (Ω X ; k ) is elliptic. Elliptic Hopf algebras G have finite depth and we show that they are characterized among Hopf algebras of finite depth by any of the following three properties: (i) ∑ i ⩽ n dim G i grows at most polynomially in n ; (ii) G is left noetherian; (iii) G is nilpotent.