What Do You Know About Semi-simplicity?
Semi-simplicity is a concept widely used in many branches of mathematics, which include representation theory, linear and abstract algebra, algebraic geometry, and category theory. An object that has semi-simplicity can be deteriorated into a total of simple objects. To know more about semi-simplicity, take this short, intelligent quiz.
- 1.
Simple objects are those that do not contain which of the following?- A.
Trivial objects
- B.
Trivial sub-objects
- C.
Non-trivial objects
- D.
Non-trivial sub-objects
- 2.
A semi-simple object is one that can be decomposed into a sum of what?
- A.
Trivial objects
- B.
Simple objects
- C.
Non-simple objects
- D.
Non-trivial objects
- 3.
What is a nonzero representation that has no proper subrepresentation?
- A.
A semi-simplicity of sets
- B.
A rigid representation of planes
- C.
An irreducible representation of an algebraic structure
- D.
A postulate of representation theory
- 4.
"Any finite-dimensional representation is a direct sum of simple representations" is a postulate of which of the following?
- A.
Representation theorem
- B.
Schur's Lemma
- C.
Maschke's theorem
- D.
Reducibility theorem
- 5.
What is semi-simplicity also called?
- A.
Multiplicity
- B.
Complete reducibility
- C.
Complete rigidity
- D.
Triviality
- 6.
Which of these describes every representation of a finite group?
- A.
Semi-simple
- B.
Simple
- C.
Non-simple
- D.
Trivial
- 7.
What is a finite-dimensional representation of a semisimple compact Lie group?
- A.
Absolute
- B.
Semisimple
- C.
Simple
- D.
Rigid
- 8.
Which is a feature of fusion category?
- A.
Flexible
- B.
Trivial
- C.
Monoidal
- D.
Non-simple
- 9.
What is a collection of objects and maps between such objects?
- A.
Category
- B.
Aggregate
- C.
Set
- D.
Concrete
- 10.
Which of these defines the following statement? While the decomposition into a direct sum of irreducible subrepresentations may not be unique, the irreducible pieces have well-defined multiplicities.
- A.
Schur's Lemma
- B.
Jordan–Hölder theorem
- C.
Holder's Theory of Multiplicity
- D.
Mackshen Theory
Questions: 12 | Attempts: 5566153 | Last updated: Mar 22, 2022
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