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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 3rd 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexcreated [[Poisson n-algebra]]

   created Poisson n-algebra

2. • CommentRowNumber2.
   • CommentAuthordomenico_fiorenza
   • CommentTimeDec 4th 2010
   • PermaLink
   Author: domenico_fiorenza
   Format: MarkdownItexit seems the natural setting for Poisson n-algebras are symmetric monoidal stable (oo,1)-categories. should we attemp a definition in that direction?

   it seems the natural setting for Poisson n-algebras are symmetric monoidal stable (oo,1)-categories. should we attemp a definition in that direction?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 5th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItex> it seems the natural setting for Poisson n-algebras are symmetric monoidal stable (oo,1)-categories. That seems right. All these operad entries could do with a more intrinsic $\infty$-description. > should we attemp a definition in that direction? Sure.

   it seems the natural setting for Poisson n-algebras are symmetric monoidal stable (oo,1)-categories.

   That seems right. All these operad entries could do with a more intrinsic $\infty$-description.

   should we attemp a definition in that direction?

   Sure.

4. • CommentRowNumber4.
   • CommentAuthordomenico_fiorenza
   • CommentTimeDec 5th 2010
   • (edited Dec 5th 2010)
   • PermaLink
   Author: domenico_fiorenza
   Format: MarkdownItexfine. what suggested me that Poisson n-algebras should have a stable oo-category version is that instead of "degree 1-n bracket on $A$" (with axioms to be specified) we could say "a Lie bracket on $\mathbf B^{n-1} A$". the next step is to convince ourselves that the oo-versions are more natural than the truncated versions (well, we should be quite convinced of this, actually :) ), and concentrate our efforts on En-algebras (the entry [[little cubes operad]] is still stubby) rather than on Poisson n-algebras.

   fine. what suggested me that Poisson n-algebras should have a stable oo-category version is that instead of “degree 1-n bracket on $A$” (with axioms to be specified) we could say “a Lie bracket on $\mathbf B^{n-1} A$”.

   the next step is to convince ourselves that the oo-versions are more natural than the truncated versions (well, we should be quite convinced of this, actually :) ), and concentrate our efforts on En-algebras (the entry little cubes operad is still stubby) rather than on Poisson n-algebras.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeDec 6th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexYes, certainly we want $E_n$-algebras, and just observe that their "classical limit" given by decategorifying by passing to homology is a Poisson $n$-algebra. I need to polish my notes at [[Hochschild cohomology]] on this point. There is some details missing where I describe the canonical $E_n$-action. I need to spend more time on that.

   Yes, certainly we want $E_n$-algebras, and just observe that their “classical limit” given by decategorifying by passing to homology is a Poisson $n$-algebra.

   I need to polish my notes at Hochschild cohomology on this point. There is some details missing where I describe the canonical $E_n$-action. I need to spend more time on that.