differential graded Lie algebra (Q15241040)
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graded Lie algebra equipped with a compatible differential
- dg-Lie algebra
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | differential graded Lie algebra |
graded Lie algebra equipped with a compatible differential |
|
Statements
![{\displaystyle {\begin{aligned}L&=\bigoplus _{i\in \mathbb {Z} }L_{i}\\\mathrm {d} &\colon L_{i}\to L_{i+1}\\{}[-,-]&\colon L_{i}\otimes L_{j}\to L_{i+j}\\{}[x,y]&=(-)^{\deg x\deg y+1}[y,x]\\0&=(-)^{\deg x\deg z}[x,[y,z]]+(-)^{\deg y\deg x}[y,[z,x]]+(-)^{\deg z\deg y}[z,[x,y]]\\\mathrm {d} [x,y]&=[\mathrm {d} x,y]+(-)^{\deg x}[x,\mathrm {d} y]\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/014834c9499e4a7ff2eeafb712d3570e73f955ea)
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Wikipedia(2 entries)
- enwiki Differential graded Lie algebra
- kowiki 미분 등급 리 대수