LIE COALGEBRAS AND RATIONAL HOMOTOPY THEORY, I: GRAPH COALGEBRAS

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Sinha D., Walter B.

HOMOLOGY HOMOTOPY AND APPLICATIONS, cilt.13, sa.2, ss.263-292, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 2
  • Basım Tarihi: 2011
  • Doi Numarası: 10.4310/hha.2011.v13.n2.a16
  • Dergi Adı: HOMOLOGY HOMOTOPY AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.263-292
  • Anahtar Kelimeler: Lie coalgebras, rational homotopy theory, graph cohomology, ALGEBRA
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We give a new presentation of the Lie cooperad as a quotient of the graph cooperad, a presentation which is not linearly dual to any of the standard presentations of the Lie operad. We use this presentation to explicitly compute duality between Lie algebras and coalgebras, to give a new presentation of Harrison homology, and to show that Lyndon words yield a canonical basis for cofree Lie coalgebras.