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Miscellaneous structures associated to algebras over operads

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1967)

In this chapter, we recall the definition of miscellaneous structures associated to algebras over operads: enveloping operads, which model comma categories of algebras over operads; enveloping algebras, which are associative algebras formed from the structure of enveloping operads; representations, which are nothing but modules over enveloping algebras; and modules of Kähler differentials, which occur in the definition of the homology of algebras over operads. In §10, we address enveloping objects and modules of Kähler differentials as examples of functors associated to right modules over operads. For the moment, we only give the definition of these structures – enveloping operads in §4.1, representations in §4.2, enveloping algebras in §4.3, Kähler differentials in §4.4 – and we study applications of these operadic constructions for the usual commutative, associative and Lie operads.

Keywords

  • Associative Algebra
  • Commutative Algebra
  • Forgetful Functor
  • Augmentation Ideal
  • Symmetric Monoidal Category

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2009 Springer-Verlag Berlin Heidelberg

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Fresse, B. (2009). Miscellaneous structures associated to algebras over operads. In: Modules over Operads and Functors. Lecture Notes in Mathematics(), vol 1967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89056-0_4

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