What Do You Know About Highest-weight Categories?

10 Questions

Settings
Please wait...
What Do You Know About Highest-weight Categories?

In mathematics, the field of representational theory studies abstract algebraic structures by the using the linear transformation of vector spaces to represent their elements. The highest weight category is also one of this representational theory, it is a k-linear category, that has k as its field. This quiz will test your knowledge about the topic and introduce you to it if you are yet to know what it is.


Questions and Answers
  • 1. 
     The highest-weight category is a field that is...
    • A. 

      Locally Artinian

    • B. 

      Functionally spaced

    • C. 

      A subset of G

    • D. 

      Geometrical

  • 2. 
    What is the concept of highest-weight categories named after?
    • A. 

      Lie group

    • B. 

      Lie algebra

    • C. 

      Boolean algebra

    • D. 

      Fourier series

  • 3. 
    If a finite-dimensional algebra has its module as the highest-weight category, what is it said to be?
    • A. 

      Uni-hereditary

    • B. 

      Para-hereditary

    • C. 

      Quasi-hereditary

    • D. 

      Tri-hereditary

  • 4. 
    Several equivalent descriptions of the ______ can be used to provide several equivalent descriptions of highest-weight categories.
    • A. 

      Abelian category

    • B. 

      Amelian category

    • C. 

      Henning category

    • D. 

      Boolean category

  • 5. 
    Who introduced the concept of highest-weight categories?
    • A. 

      Parshall, Davis and Craig

    • B. 

      Davis, Craig and Cline

    • C. 

      Cline, Steve and Davis

    • D. 

      Parshall, Scott and Cline

  • 6. 
    What can monomorphism also be called?
    • A. 

      Embeddings

    • B. 

      Epimorphs

    • C. 

      Retraction

    • D. 

      Unimorphism

  • 7. 
     A category is Abelian if it has how many objects?
    • A. 

      Four

    • B. 

      Three

    • C. 

      Two

    • D. 

      One

  • 8. 
    Which is one of the characteristics of the highest-weight categories?
    • A. 

      Polymorphisms are unique for every function

    • B. 

      Zero objects are unique up to isomorphism

    • C. 

      Both A and B

    • D. 

      Neither A and B

  • 9. 
    What must the highest-weight category have?
    • A. 

      Simple injectives

    • B. 

      Enough injectives 

    • C. 

      Infinite subsets

    • D. 

      Boolean algebra

  • 10. 
    The representational theory is a mathematical subject that looks to study symmetries in...
    • A. 

      Scalar spaces

    • B. 

      Vector spaces

    • C. 

      Scalar spaces

    • D. 

      Radial spaces