# What Do You Know About Subrepresentations?

10 Questions | Total Attempts: 102  Settings  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.

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

Representation theory

• B.

Maxim theory

• C.

Algebraic theory

• D.

• 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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