Elliptic Hopf Algebras | Zendy

Félix Yves | Zendy; Halperin Stephen | Zendy; Thomas JeanClaude | Zendy

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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.

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