Math 4010 & 5530 Section 101 Homepage

News & Announcements

Term Project Ideas: More suggestions later...or come up with one of your own!
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  1.  The connection between a Lie group and a Lie algebra.

  2.  The universal enveloping algebra and PBW theorem.

  3.  Constructing the exceptional algebra G2.

  4.  Representation theory of sl3=A2 (especially weight multiplicities).

  5.  Formal calculus (background for vertex algebras)

  6.  Kac-Moody Lie algebras (generalized Cartan matrices)



Term Project Topics Reserved:

    

  1.  Matthew Jobrack & Kent Vashaw = Solvable Lie algebras and Lie's Theorem

  2.  Brett Boyles, Sydney Carter, & Amanda Yoder = Nilpotent Lie algebras & Engel's Theorem

  3.  Noah Hughes = Formal Calculus & Vertex Algebras

  4.  Ethan Smith & Tessa McMullen = Universal enveloping algebras & the PBW Theorem

  5.  Michael Kelley & Jacob (Genuine Tyrel) Winebarger = Coxeter Groups (A Generalization of Weyl Groups)

  6.  Anthony-James "TJ" Kerns (i.e. Fake Tyler) & Walter Bridges = Connections between Lie groups and algebras

  7.  ??John Adkins, Ashley McBride, & Cory Benfield?? = The Killing form and Cartan's Criterion (I and II)

  8.  Nathan Green = Heisenberg Lie Algebra(s)

  9.  Margaret Haskell & Rodney Payne = Simple Lie algebras of type B_n = so(2n+1)



12/03 Root Systems in Maple (.mw) 
      This worksheet will plot Dynkin diagrams, weights for irreducible representations
      for simple Lie algebras of ranks 1, 2, and 3. It will also find Cartan matrices,
      simple roots, fundamental weights, highest long roots, and do Weyl group computations.

12/02 Final Project Rubric

      LaTeX Examples

11/22 Noah spotted a problem with the grad problem: A maximal submodule is a
      PROPER submodule such that there are no modules between it and the
      whole module. Anyway, I left off the condition "proper" (which rules out V=M).

      Sorry!



11/21 A big thanks to Noah for letting me post his solutions!!
      [withdrawn for now]
      

11/11 We will have Big Quiz #2 on Friday, November 22nd.

      Homework #2X is due Monday, November 18th.
      [For those who LaTeX, Homework #2X (.tex).]

10/30 Homework #1X is due Friday, November 8th.
      [For those who LaTeX, Homework #1X (.tex).]

09/30 Hi everyone,

      I had made a typo on number 5, so I ask that you do read section 3.2.2 
      in your textbook before friday, but you do not need to complete problem 
      number 5. 

      In case you are interested it should have read:

      L is isomorphic to A oplus B there A is the 2-dimensional non-Abelian 
      Lie algebra and B is the trivial one-dimensional Abelian Lie algebra.

      -Vicky

09/20 Hi everyone,

      I forgot to tell you when the take home part of the big quiz is due.  
      It will be due on Wednesday.  Also, please remember that for the take-home 
      part it is o.k. to talk to each other about the problems.

      And Matt pointed out a typo in the first sentence of the graduate problem.  
      It should read:

      Let F[x] be the ring of polynomials in x with coefficients in the field F.

      -Vicky

09/11 Schedule for classes 1-15 (including suggested homeworks & readings)

08/30 I have slightly adjusted my office hours...

      Mondays from 9:00 9:30am until 10:00am
      Tuesdays 9:00am until 11:00am & 2:30pm until 5:00pm
      Wednesdays & Fridays from 9:00am until 10:00am

08/21 Homework #1 due Wed. Sept. 4th

      Schedule for classes 1-5 (including suggested homeworks & readings)

08/14 Syllabus [Syllabus for MAT 5530], schedule, and suggested homework have been posted.

      Dr. Klima will post relevant materials on a href="https://asulearn.appstate.edu" target=_top>AsULearn. During her portion
      of the class, please look there first!

      Please note: If homework webpages don't print well, you
      can download a package of fonts to help things look better.
      The fonts (and installation instructions) can be found here.
      For PCs: PC jsMath fonts and 
      For Macs: Mac jsMath fonts

      Some old 2240 handouts: 
      Gauss-Jordan Elimination & The Linear Correspondance
      Finding & Extending Bases Example
      Coordinate Matrix Example
      Kernel, Range, Composition of Linear Transformations Example
      Eigenhandout

      Course Data
      MAT 4010 Section 101 & MAT 5530 Section 101
      INTRO TO LIE ALGEBRAS
      Meeting Times MWF 09:00am-09:50am
      Room WA 308

      Course Title & Description:
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      MAT 4010-101 & 5530-101 "Introduction to Lie Algebras" 3 credits
 
      Prerequisite: 3110

      Title: "Introduction to Lie Algebras"

      This course will be co-taught by Vicky Klima and Bill Cook. 
      Dr. Klima will be teaching the first half and Dr. Cook the second.
      
      After some intermediate linear algebra background, we will look
      at the basic theory of Lie algebras including the definition,
      examples, subalgebras, homomorphisms, quotients. Then we will 
      transition to some representation theory discussing the definition
      of a representation/module, module maps, Schur's lemma, sl2 
      representation theory, Weyl's theorem, the root space decomposition 
      of simple Lie algebras, root systems, Weyl groups, Cartan matrices,
      Dynkin diagrams, and the classification of simple Lie algebras. 
      
      Time permitting, we will also look at irreducible representations 
      of simple Lie algebras, the weight space decomposition, and the
      classification of these irreducible representations.
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      Any questions about this class? 
      Send me an email at cookwj@appstate.edu