On Hopf algebra structures over free operads |
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Authors: | Ralf Holtkamp |
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Institution: | University of Bochum, 44780 Bochum, Germany |
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Abstract: | The operad Lie can be constructed as the operad of primitives PrimAs from the operad As of associative algebras. This is reflected by the theorems of Friedrichs, Poincaré-Birkhoff-Witt and Cartier-Milnor-Moore. We replace the operad As by families of free operads P, which include the operad Mag freely generated by a non-commutative non-associative binary operation and the operad of Stasheff polytopes. We obtain Poincaré-Birkhoff-Witt type theorems and collect information about the operads PrimP, e.g., in terms of characteristic functions. |
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Keywords: | 16W30 17A50 18D35 18D50 |
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