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Maurer–Cartan element of a complete filtered L∞-algebra
Definition
For a complete filtered L∞-algebra in the convention of Complete filtered L∞-algebra, a Maurer–Cartan element is an element satisfying
The series is the unique limit proved in The Maurer–Cartan series converges in a complete filtered L∞-algebra. This equation defines a set of solutions; it does not by itself specify a deformation problem or an equivalence relation on those solutions.
Depends on
Used by
- The Maurer–Cartan equation alone does not specify gauge classes Counterexample
- Completed polynomial gauge paths for filtered Maurer–Cartan elements Definition
- A finite complete filtered L∞ Maurer–Cartan equation Example
- The general Maurer–Cartan deformation correspondence needs a proved gauge construction Remark
- Filtered L∞-morphisms preserve Maurer–Cartan elements and compose on solutions Theorem
Dependency tree · two levels
6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Jean-Louis Loday and Bruno Vallette, Algebraic Operads, §13.2 (standard reference, not scraped)