Further results on q-Lie groups, q-Lie algebras and q-homogeneous spaces

Abstract We introduce most of the concepts for q -Lie algebras in a way independent base field K . Again it turns out that we can keep same Lie algebra with small modification. use very similar definitions all quantities, which means proofs are similar. In particular, quantities solvable, nilpotent, semisimple algebra, Weyl group and chamber identical ordinary case = 1. The computations sample -roots certain well-known groups contain an extra -addition, consequently, -deformed, add prefix respective name. Important examples -Cartan subalgebra Killing form. concept q- homogeneous spaces formal exemplified by S U q ( 1 , ) O 2 {{S{U_q}\left( {1,1} \right)} \over {S{O_q}\left( 2 \right)}} 3 {{S{O_q}\left( 3 corresponding -geodesics. By introducing -deformed semidirect product, define exact sequences some other interesting -homogeneous spaces. give example -Iwasawa decomposition SL (2).