id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ap-926	Burdík, Č.; Navrátil, O.; Pošta, S.	Structure of the Enveloping Algebras	2007	7	.pdf	application/pdf	5891	142	64	If we want to study all two-sided ideals of the associative algebra U (see [1] chapters 6–10), i.e. to find all the vector spaces I U� which satisfy for all a b U aIb I, :� � we can easily see that such a two-sided ideal is invariant with respect to adjoint action of U: if we take adjoint action � : ( )g L U� , i.e. �( ) [ , ]x a x a� for x g� and a U� and extend this definition to all U by � �� �� � �( ) ( ) ( ) , , [ , ]u x x x x an n� �1 1� � � for all u x x x gn i� �1� , we see that �( ) The simplest example – algebra sl(2) Let us have algebra sl(2) which is a complex linear span of three vectors E E H E E12 21 1 11 22, , � � , where by Eij we denote the matrix having 1 in position (i, j) and 0s elsewhere.	cache/ap-926.pdf	txt/ap-926.txt