En matemáticas , un álgebra de Lie anónica es un espacio vectorial graduado U (1)
encima
equipado con un operador bilineal
y mapas lineales
(algunos autores usan
) y
tal que
, satisfaciendo los siguientes axiomas: [1]
![\ varepsilon ([X, Y]) = \ varepsilon (X) \ varepsilon (Y)](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
![{\ Displaystyle [X, Y] _ {i} \ otimes [X, Y] ^ {i} = [X_ {i}, Y_ {j}] \ otimes [X ^ {i}, Y ^ {j}] e ^ {{\ frac {2 \ pi i} {n}} \ varepsilon (X ^ {i}) \ varepsilon (Y_ {j})}}](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
![{\ Displaystyle X_ {i} \ otimes [X ^ {i}, Y] = X ^ {i} \ otimes [X_ {i}, Y] e ^ {{\ frac {2 \ pi i} {n}} \ varepsilon (X_ {i}) (2 \ varepsilon (Y) + \ varepsilon (X ^ {i}))}}](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
![{\ Displaystyle [X, [Y, Z]] = [[X_ {i}, Y], [X ^ {i}, Z]] e ^ {{\ frac {2 \ pi i} {n}} \ varepsilon (Y) \ varepsilon (X ^ {i})}}](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
para graduadas puro elementos X , Y , y Z .