Recent content by valtz

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    Graduate Three dimensional Lie algebra L with dim L' = 1

    Now suppose the derived algebra has dimension 1. Then there exits some non-zero X_{1} \in g such that L' = span{X_{1}}. Extend this to a basis {X_{1};X_{2};X_{3}} for g. Then there exist scalars$\alpha, \beta , \gamma \in R (not all zero) such that [X_{1},X_{2}] = \alpha X_{1} [X_{1},X_{3}] =...
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    Graduate What Are the Axioms and Identities for Two-Dimensional Lie Algebras?

    thanks for your answer , i understand now about two dimensional lie algebra but can u give "real(not field)" example two dimensional non abelian lie algebra , from what vector space to what? and lie bracket define in there... thanks guys my essay is about lie algebra, sorry if I'm a...
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    Graduate What Are the Axioms and Identities for Two-Dimensional Lie Algebras?

    can u give me some example for two dimensional lie algebra?
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    Graduate What Are the Axioms and Identities for Two-Dimensional Lie Algebras?

    I read in mark wildon book "introduction to lie algebras" "Let F be any field. Up to isomorphism there is a unique two-dimensional nonabelian Lie algebra over F. This Lie algebra has a basis {x, y} such that its Lie bracket is described by [x, y] = x" and I'm curious, How can i proof...
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    Graduate Proving Theorem 51.3 in Munkres 2e Edition on Homotopy Paths

    i stuck when i want to prove theorem 51.3 in munkres 2en editions about homotopy paths Let f be a path in X , and let a0 , ... , an be numbers such that 0= a0 < a1 < ... < an. Let fi : I → X be the path that equals the positive linear map of I onto [ai-1, ai] followed by f then [f] = [f1]...