The Conclusions And The Nature Of The Q-lie Algebra

We have been up on Lie algebra,so the text will study a special Lie algebra--q-Lie algebra.The q-Lie algebra is also a spread of Lie algebra and define q-Lie bracket product which correlates q.The definition of Lie bracket product brings about lots of conclusion and character which are similar with the general Lie algebra's,however,because of the special character of q-Lie algebra,it has some new content and so the text will mainly study the q-Lie algebra's conclusion and character.Fist of all,the text give some q-Lie algebra's concept,for example q-Lie subalgebra,q-Lie quotient algebra,q-normalizer,q-centralizer,which prepares for the latter content.Because the solution and nilpotent are very important to every algebra and have some important effect,we give the definition of idea and imitate Lie algebra to study q-Lie algebra's solution and nilpotent.Next,in order to make clear the origin and tectonic of q-Lie algebra,we can construct q-lie algebra similarly by the general association algebra and the test gives the necessary condition of being a q-lie algebra.Then,we give a example to prove that the tectonic is reasonable.When we study a algebra,we should make clear of it's structure.If two algebras are isomorphism,the two algebras are thought the same.Because more dimension q-lie algebra is not easy to analyze,we analyze concretely 1 and 2 dimension q-lie algebra.That can further perfect the q-lie algebra.In the final of the text,we give the definition of universal enveloping algebra and discuss its nature.In the last,we give a important example of q-lie algebra.Overall,the text further study q-lie algebra's nature and conclusion on base of predecessors' work.Because learning is endless,there is lots of content interrelating to the text to solve.