Bala-bala Lie algebras

August 16, 2008 at 1:40 am | Posted in Math Learning | 1 Comment
The cover of "Introduction to Lie algebras and Representation Theory", translated by Jui-Ji Chang

Introduction to Lie algebras and Representation Theory, translated by Jui-Ji Chang

Gee was so happy to met Jyun-Ao , a student of  Shun-Jen, remind me to pick my memory about Lie algebras…  It had been several years since I was struggle for knowing what’s the key math touch my mind. Lie algebras was really a unexpected beauty for me. The history of me to touch Lie algebras maybe an accident(or not)…

  • Beginning, Wen Long Lin who taught Applied mathematics in department of physics shows me two books of Lie algebras in 2001. Which are:(A)Howard Gergi. Lie Algeras in Partical Physics(1999). ISBN:0-738-20233-9. (B)Robert . Chahn. Semi-Simle Lie Algebras & their Representations.BenJamin/cummings(1984). ISBN:0-805-31600-0. …He said “Department of Mathematics may be better than Department of Physics if you want to learn these.”… Did not agree with him that time because I never saw or learned Lie algebras in Department of Mathematics till met him.
  • Found what “root system”is of the paper on the webpage I saw in 2004 : Valentina Golubeva:Hamiltonians of the Calogeto-Sutherland Type Models Associated to the Root Systems and Corresponding Fock Spaces….For understanding this paper and others I did not mention here, I was been kicked out the door of Roger. It became a penal pain pricked my heart that hard to be cured in my memory…
  • Audit a course of Chia-Hsin Liu to know root systems, He used the Humphreys’ book… There is no feelings happened in my mind in his class, thus gave the course up immediately…Audit his class just one time…For knowing that course did open for those  interested in ideal and rings.
  • The story after baby lie groups(class of Chun Chung in 2004) and lie group(class of Ong, Ping-Zen) attract me, especially for the class of Chun Chung, Lie algebras just like the drum in heaven that drumed me…
  • Met I-Hsun in 2004. Wanted to go to his Differential Geometry course to listen more things about Lie algebras but fixed in the Lie algebras course of Shun-Jen for one year.
  • ??—to present.

m…m… let me talk about translation works of mathematics.  After doing “My oops translate“, I felt a little better. But offer such volunteer effort really not a work or plan that should be do. Anyway I get something I like to do from doing that… It’s a long time not touch math, this way can cure my life a moment…Good translation is not a easy work, especially for mathematics. Take my translating “18.238 Geometry and Quantum Field Theory, Fall 2002” for example, I never know what I type…Just a machine kala~ka-la.  Keep the questions in your stomach or you cannot finish the document.

Borrowed the book,「張瑞吉 譯。李代數與表現理論之導引。國立編譯館主編。台北:黎明文化(民70)。」which is translated from the famous book: “Jumes E. Humphreys. Introduction to Lie Algebras and Representation Theory, GTM9. Springer-Verlag New York,1972.” ,from Taitung County library.  Prof. Rui-Ji Chang translate the book very well. Didn’t know if the teachers in the university before like translate. Gee regard them are all tips on tops during those days. They wrote, edited and translated excellent books by themselves…seems a little different than present day. Anyway,Each period must exist its great events.Back to translate…

Because of the translation mistake always happened for general translation. Gee still like read the original version than the second. Even for this good book translated by Prof. Chang…


J. E. Humphreys wrote…

Definition. A vector space L over a field F, with an operation L × L→L, dented (x,y) →[xy]and called the bracket or commutator of x and y, is called a Lie algebra over F if the following axioms are satisfied:

(L1) The bracket operation is bilinear.
(L2) [xx]=0 for all x in L
(L3)[x[yz]]+[y[xz]]+[z[xy]]=0 (x,y,z∈L)

Rui-Ji Chang translated

定義 設 L 為體 F上的向量空間,而 L × L→L為L中的一個運算,記為 (x,y) →[xy]稱為x與y的括弧或換位元素。再設這個括弧運算滿足下列公理:

(L1) 括弧運算為雙線性。
(L2)[xx]=0 對所有 x ∈ L。
(L3)[x[yz]]+[y[xz]]+[z[xy]]=0 (x,y,z∈L)


You catch the points here? That’s why I like to read the original book than the translated one, even though the Chinese words are so cute for me. Each translated book like this must have the tiny mistakes like these~ They will confuse me a lot to read the book (From these, you may understand that “to read a book well” is such a difficult hobby for me><).

For being an oops mathematic courses translator…Keep learning is an important things. Even though the problems also a lot, and lots problems like the upper statement…

“Just Go!” give myself the words!! I will be a good translator like Rui-Ji.


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  1. […] Definition. A Lie algebra is an algebra g which operation[,] satisfied [x,x]=0 and Jacobi identity…(please click Bala-bala Lie Algebras). […]

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