What Do You Know About Subrepresentations?

10 Questions | Total Attempts: 102

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What Do You Know About Subrepresentations?

Representations—in the representation theory branch of mathematics—have subrepresentations. They simply mean a representation with limited dimensions dependably contains a nonzero subrepresentation that is unchangeable. Also, given a representation of a group, a direct linear subspace is preserved by a predefined action. If you'd like to know more about subrepresentations, take the short quiz below.


Questions and Answers
  • 1. 
    What are irreducible representations the building blocks of?
    • A. 

      Representation theory

    • B. 

      Maxim theory

    • C. 

      Algebraic theory

    • D. 

      Quadratic function 

  • 2. 
    When V has exactly two subrepresentations, namely the trivial subspace {0} and V itself, then the representation is said to be what?
    • A. 

      Irreducible

    • B. 

      Functional

    • C. 

      Maximal

    • D. 

      Reducible

  • 3. 
    Which theory states that the process of decomposing a tensor product as a direct sum of irreducible representations? 
    • A. 

      Choquet theory

    • B. 

      Braid theory

    • C. 

      Clebsch–Gordan theory

    • D. 

      Maxim theory

  • 4. 
    Which of these arises in the applications of finite group theory to geometry and crystallography?
    • A. 

      Group representation

    • B. 

      Maximum functions

    • C. 

      Functional numbers

    • D. 

      Irreducible representation

  • 5. 
    When the representation of a finite group G has a number of convenient properties it is known as?
    • A. 

      Finite zero

    • B. 

      Maxim point

    • C. 

      Characteristic zero

    • D. 

      Functional stop

  • 6. 
    What types of fields does Maschke's theorem prove?
    • A. 

      Field of an angle

    • B. 

      Positive characteristics

    • C. 

      Line function

    • D. 

      Algebraic fields

  • 7. 
    How are representations of a finite group G linked directly to algebra?  
    • A. 

      Group algebra

    • B. 

      Finite point

    • C. 

      View point

    • D. 

      Misrepresentations

  • 8. 
    Which characteristics do Lie groups have?
    • A. 

      Finite numbers

    • B. 

      Smooth manifold

    • C. 

      Irregular manifold

    • D. 

      Complex functions

  • 9. 
    In which field is representation theory ideal?
    • A. 

      Linear algebra

    • B. 

      Solving functions

    • C. 

      Angular calculations

    • D. 

      Complex functions

  • 10. 
    What does the vector space V denote in representation analysis? 
    • A. 

      Representation space

    • B. 

      Representation dimension

    • C. 

      Algebraic constant

    • D. 

      Representation line

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