Afissar n Lie Algebra
Context:Dǎɣ maɗinan, tartit tan Lie taqalat tartit tan Lie winan eqel abélienne G winan ila daw-titibawen atiwasanan winan eqel aśohen. Tabarat ən tartiten ən Lie raqisnen adobatnat adiqilan amitkalan fal adakal ən tabarat ən algèbretan ən Lie raqisnen əd dagan ən simetrik ən Riemannian.  Dǎɣ tartit ən tartit tan Lie ən maɗinan adutətnen, "R"" d win unit-magnitude complex numbers, U""1) (unit circle), taqqimen n Lie raqqosnen hak nat atomic "blocks" ijjan taqqimen n Lie fuk (ilsanat iddikud) s alxidmat n asidu n taqqimt "Kel harkuk, taqqimen n Lie ajjotnen oharnen aqqalan a oharnen meɣ a oharnen"": almital, awa s itawan ""taqqimt n iyaka tan iyaka"" SL ((n) n n by n matrices s determinant ogdah nen s 1 eqqal a oharnen i n > 1 fuk"  Təmusne tazarat ən tartiten ən Lie raqisan taqal atiwagan fal Wilhelm Killing, əd əšiɣil wen eqal ayknan darat awa fal Élie Cartan. Anmizlay wan uchray eqqal alwaq iyyan isim net Killing-Cartan
War t illa almaɣna n taqqimt n Lie raqqisan Dǎɣ təbiɗawt, winan eqel harkuk atiwalaɣat sund tartit tan Lie taqalat raqisat sund tartit taqalat winan atwazay. Əmigridan abdanen fal as tartit tan Lie taqalat adizgaran, meɣ fal as taqalat atiwafan ye adiqil aylan amas winan eqel ayknan, meɣ fal as <unk>mǝli Eqal taqqimt taśohet ən Lie.  Almaɣna wa oharan amos as taqqimt tan Lie taqqal raqqis a fal osaɣan, war n aqqel Abelian tolas taqqimt fuk ta s itawan osaɣan eqqal anmizlay meɣ taqqimt fuk Dǎɣ təbiɗawt, tartiten tən banan aqalnen atiwagan fal adiqilan aylan amas ən winan eqel aśohen, mašan <unk>mǝli War eqqel harat raqqisan  Daɣ artikl wen, taqqimen n Lie raqqosnen osaɣnen id ammas n trivial iknanat akatab Alwaq wa id issanan win, wi war n aqqel wi madroynen daɣ ammas aqqalan a olaɣan i asidu chund awen Taqqimt fuk n Lie s ammas net war n ila almaɣna tila asidu n alɣalim, s ammas net eqqal taqqimt ta tazzarat n taqqimt n Lie Taqqimen n Lie tin raqqisnen s ammas war n oɣed addobat nat ad aj in s quotient tan n cover wen n alɣalim s taqqimt andarrat n ammas  Dumu tan iyyad Almaɣna ogdahan n taqqimt n Lie raqqisan ilkam i almaɣna n Lie: taqqimt n Lie osaɣan raqqis a fal Lie algebra net raqqis Titbaqqet maqqorat n musnat taqqal as taqqimt n Lie raqqisat addobat a ti illa subgroups n normal Fal tidit ten, almaɣna n taqqimt n Lie raqqis war ogdah id almaɣna n taqqimt n Lie raqqisat chund taqqimt ta toɣadat  Taqqimen n Lie raqqosnen ahanat taqqimen n Lie ajjotnen n alasal, hakkinen taqqimt n mirda i spherical geometry, projective geometry d geometry tan osaɣan daɣ almaɣna wan Felix Klein's Erlangen program Ijja ɣur asidu n askut n taqqimen n Lie raqqosnen as illanat deɣ tiyyad addobat nen n a war n ogdah id geometry fuk Taqqimen tin war n oherat aqqalan almital tan ajjotnen d ikayadan daɣ ihandagan iyyad n matematik hak id physics tan theory tan amarad  Daɣ almital, taqqimt tan iyaka war taqqel raqqis meɣ semisimple Awen fal as multiples n tumast taqqal nat taqqimt andarrat n normal war n oɣed, daɣ awen asidu n almaɣna Dǎɣ olahan, algèbre tan Lie taqalat əmik ən Killing amutayan, falas anilkaman ən əmik ən amutiy ən əmik wan wala ən algèbre. Dǎɣ awen, algèbre tan Lie taśohet intanedǎɣ war eqel deɣqanen aśohen meɣ abdanen. Almital iyyan eqqalan taqqimen n orthogonal daɣ iddikud olaɣan Awen ila matrix - awa id eqqalan <unk>mǝli -I daɣ ammas tolas titbaqqet ten eqqal a orakan s titbaqqet n tumast tolas taqqimen tin tijja almaɣna Issin haratan win aqqalan taqqimen afanaz nen