What Do You Know About The Stable Module Category?

10 Questions | Total Attempts: 106

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What Do You Know About The Stable Module Category? - Quiz

In the representation theory branch of mathematics, the stable module category is is a classification or category with projectives that are considered out. If you would like to know more about this widespread type of categories, let's asses your knowledge of the stable module category by taking this short, intelligent test.


Questions and Answers
  • 1. 
    How can you describe the projectives?
    • A. 

      Factored in

    • B. 

      Factored out

    • C. 

      Reduced

    • D. 

      Optimised

  • 2. 
    What is a vector space together with a non-associative bilinear map?
    • A. 

      Lie group

    • B. 

      Lemma

    • C. 

      Lie algebra

    • D. 

      Weyl's constant

  • 3. 
    Which property of a binary operation describes how the order of evaluation affects the result of the operation?
    • A. 

      Konstant function

    • B. 

      Weyl character

    • C. 

      Weyl's constant

    • D. 

      Jacobi identity

  • 4. 
    What is a function that has derivatives of all orders everywhere in its domain?
    • A. 

      Smooth function

    • B. 

      Linear function

    • C. 

      Rigid function

    • D. 

      Associative function

  • 5. 
    What is the classification of functions according to the properties of their derivatives?
    • A. 

      Multiplicity class

    • B. 

      Differentiability class

    • C. 

      Reducibility class

    • D. 

      Associativity class

  • 6. 
    Which is not a feature of a Lie bracket?
    • A. 

      Bilinear

    • B. 

      Alternative

    • C. 

      Anti-commutative

    • D. 

      Rigid

  • 7. 
    Levi's theorem says that a finite-dimensional Lie algebra is a semidirect product of its radical and what?  ​​​​​The... 
    • A. 

      Complementary subalgebra

    • B. 

      Supplementary algebra

    • C. 

      Supplementary algebra

    • D. 

      Smooth subalgebra

  • 8. 
    If the lower central series of a Lie algebra becomes zero eventually, what is it termed?  
    • A. 

      Bilinear

    • B. 

      Nilpotent

    • C. 

      Reducible

    • D. 

      Original

  • 9. 
    If a Lie algebra has no non-trivial ideals and is not abelian, what is it termed?
    • A. 

      Trivial

    • B. 

      Original

    • C. 

      Simple

    • D. 

      Rigid

  • 10. 
    If a Lie algebra is isomorphic to a direct sum of simple algebras, what is it called?
    • A. 

      Trivial

    • B. 

      Original

    • C. 

      Simple

    • D. 

      Semi-simple

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