Monoidal Hom–Hopf Algebras

By Stefaan Caenepeel, I. Goyvaerts. 2009

216 citations recorded by the source corpus.

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal category such that Hom-algebras coincide with algebras in this monoidal category, and similar properties for coalgebras, Hopf algebras, and Lie algebras.

View Paper: https://www.semanticscholar.org/paper/9b720f6b9062c8f468378f13449c6c3512f19b93

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Citations in the corpus

• Rota–Baxter Hom-Lie–Admissible Algebras (2011, background): “Further development could be found in, for example, [34, 56, 57, 7, 9, 56, 15, 46],[68]-[73], and the references therein.”
• BiHom-associative algebras, BiHom-Lie algebras and BiHom-bialgebras (2015, methodology): “When G = Z, c = d = 1Z and ν = id1 one gets the category H(C) from [8], while for c = 1Z, d = −1Z and ν = id1 one gets the category H̃(C).”
• Yetter-Drinfeld modules for Hom-bialgebras (2013, methodology): “The H-linearity of aM,N,P follows from the computation performed in [6], proof of Proposition 2.”