Schreiber
generalized smooth L-infinity algebroid

Idea

Generalized smooth L L_\infty-algebroids, or C C^\infty-L L_\infty-algebroids, are supposed to be the correct Lie theory-dual of infinity groupoids internal to generalized smooth spaces, Spaces:=Sheaves(CartesianSpaces)Spaces := Sheaves(CartesianSpaces).

Following the general lore of Space and Quantity and hence using the notion of generalized smooth algebras, a generalized smooth L L_\infty-algebroid should be just like an L-infinity algebroid but with its defining Chevalley-Eilenberg algebra realized internal to Quantities:=CoPrSh(CartesianSpaces)Quantities := CoPrSh(CartesianSpaces):

the algebra of functions is taken to be a C-infinity-algebra and the complex of modules is taken to be a complex of C-infinity modules.

Revised on May 29, 2012 22:04:00 by Andrew Stacey (129.241.15.200)