What Do You Know About Hopf Algebras?

10 Questions

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What Do You Know About Hopf Algebras?

A Hopf algebra is a bialgebra (unit associative algebra and co-unital associative algebra) that is equipped with an antiautomorphism to satisfy a property. It is one of the mathematical representational theories and it is studied especially with several works on special classes of examples and classification problems. In almost every field in mathematics, Hopf theorem needs to be studied--but with this quiz, you can get an idea of what it's all about.


Questions and Answers
  • 1. 
    Who was Hopf named after?
    • A. 

      Heinz Hopf

    • B. 

      Lucas Hopf

    • C. 

      Hermes Hopf

    • D. 

      Herman Hopf

  • 2. 
    The representation theory of Hopf algebra allows for construction of the following except one; which one?
    • A. 

      Trivial representations

    • B. 

      Dual representations

    • C. 

      Tensor products of representation

    • D. 

      Bilateral representation

  • 3. 
    What of these do Hopf algebras have NO application in?
    • A. 

      Quantum field theory

    • B. 

      String theory

    • C. 

      Projectiles

    • D. 

      LHC phenomenology

  • 4. 
     If the antipode S2 = idH, the Hopf algebra is said to be what?
    • A. 

      Evolutive

    • B. 

      Involutive

    • C. 

      Finite

    • D. 

      Infinite

  • 5. 
    One of the notions of Hopf algebra is that it is an abstraction of properties of which of these?
    • A. 

      Lie algebra

    • B. 

      Boolean algebra

    • C. 

      Fourier algebra

    • D. 

      Group algebra

  • 6. 
    What is the unit of Hopf algebras?
    • A. 

      Single elements

    • B. 

      Multi-elements

    • C. 

      Poly elements

    • D. 

      Group-like elements

  • 7. 
    A group-like element is a _______ element.
    • A. 

      Non-zero

    • B. 

      Zero

    • C. 

      Prime

    • D. 

      Linear

  • 8. 
    A finite groupoid algebra is categorized as what? A...
    • A. 

      Weak Hopf algebra

    • B. 

      Strong Hopf algebra

    • C. 

      Dual Hopf algebra

    • D. 

      Group Hopf algebra

  • 9. 
    If G is taken to be a set instead of a module, the field K will be replaced by what? A/an...
    • A. 

      3-point set

    • B. 

      2-point set

    • C. 

      1-point set

    • D. 

      0-point set

  • 10. 
    What is the property defined by E: H -> R?
    • A. 

      Co-commutative

    • B. 

      Co-additive

    • C. 

      Comultiplication

    • D. 

      Commutative