What Do You Know About Subrepresentations?

10 Questions | By AdeKoju | Last updated: Mar 18, 2022 | Total Attempts: 107

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What Do You Know About Subrepresentations? - Quiz

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