Take Our Quiz About The Representation On Coordinate Rings

10 Questions | Total Attempts: 101

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Take Our Quiz About The Representation On Coordinate Rings - Quiz

For those who love mathematics, representation on coordinate rings is defined as the representation of a group on coordinate rings of affine varieties. Now, the question is do you know all the symbols and terms involved with this discipline? Do you use them in your every day life? Take our quiz and see if you really know what a representation on coordinate rings is.


Questions and Answers
  • 1. 
    What's an Affine algebraic variety?
    • A. 

      It's the affine n-space K^n

    • B. 

      It's the equivalent of K^n

    • C. 

      It's simply the n-space

    • D. 

      It's the zero-locus in the affine n-space K^n

  • 2. 
    What's a reductive group?
    • A. 

      It's a type of linear algebraic group over a field.

    • B. 

      It's a type of line of group over a field.

    • C. 

      It's a type of linear algebraic group over a curve.

    • D. 

      It's a type of continuous algebraic group over a field.

  • 3. 
    What's a symmetric variety?
    • A. 

      It's an algebraic analogue of a symmetric space in general.

    • B. 

      It's an algebraic analogue of space in differential geometry.

    • C. 

      It's the symmetrical space in differential geometry.

    • D. 

      It's an algebraic analogue of a symmetric space in differential geometry.

  • 4. 
    What's a spherical variety?
    • A. 

      It's an A-variety with an open dense B-orbit

    • B. 

      It's a B-variety with an open dense B-orbit

    • C. 

      It's a G-variety with an open dense B-orbit

    • D. 

      It's a B-variety with an open dense A-orbit

  • 5. 
    What's a matrix coefficient?
    • A. 

      It's a function on a group of a special form, which depends on a representation of some additional data.

    • B. 

      It's a function on a group of a special form, which depends on a linear representation of the group and additional data.

    • C. 

      It's a function on a group, which depends on a representation of the group and additional data.

    • D. 

      It's a group of a special form, which depends on a linear representation of the group and additional data.

  • 6. 
    What's the Peter-Weyl theorem?
    • A. 

      It's a basic result in the theory of harmonic analysis applying to topological groups that are compact but are not necessarily real numbers.

    • B. 

      It's a basic result in the theory of harmonic analysis applying to topological groups that are liquid but are not necessarily abelian.

    • C. 

      It's a basic result in the theory applying to topological groups that are solid but are not necessarily abelian.

    • D. 

      It's a basic result in the theory of harmonic analysis applying to topological groups that are compact but are not necessarily abelian.

  • 7. 
    What's a complex number?
    • A. 

      It's a number that can be expressed in the form a-bi

    • B. 

      It's a number that can be expressed in the form a+bi

    • C. 

      It's a number that can be expressed in the form b+ai

    • D. 

      It's a number that can be expressed in the form c+bi

  • 8. 
    What's a real number?
    • A. 

      It's a valve of a continuous quantity that can represent a distance along a line.

    • B. 

      It's a valve of a continuous quantity that can represent a distance along a curve.

    • C. 

      It's a valve of a continuous quantity that can represent a distance along a circle.

    • D. 

      It's a valve of a constant quantity that can represent a distance along a line.

  • 9. 
    What's the other term for a polynomial ring?
    • A. 

      Polynomial mathematics

    • B. 

      Polynomial algebra

    • C. 

      Polynomial bond

    • D. 

      Polynomials

  • 10. 
    What's the other term for an eigenvector?
    • A. 

      Eightvector

    • B. 

      Vectors

    • C. 

      Characteristic vector

    • D. 

      Sevenvector

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