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Showing 1 to 2 of 2 for “"Operad theory"”.
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Connecting models of configuration spaces: From double loops to strings
<p>Foundational to the subject of operad theory is the notion of an <em>En</em> operad, that is, an operad that is quasi-isomorphic to the operad of little <em>n-</em>cubes <em>Cn.</em> They are central to the study of iterated loop spaces, and the specific case of <em>n</em> = 2 is key in the …
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The Koszul dual to n-Lie, n-Com algebras, and Young tableaux
We study the operad $n\text{-}Lie_d$, whose algebras are $n$-Lie algebras, which was first introduced in Nambu mechanics to extend Hamiltonian mechanics to more than one Hamiltonian. We find the Koszul dual of $n\text{-}Lie_{-d+n-2}$ to be the operad $n\text{-}Com_d$, whose relations come from the …