What Do You Know About The Root Datum?

10 Questions | Total Attempts: 104

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What Do You Know About The Root Datum? - Quiz

Considered and introduced by Michel Demazure in the 1970s, the root datum is a widely used approach in the group theory branch of mathematics. It is a speculation of a root system or framework that decides the gathering up to isomorphism. This generally means the the root datum of a linked break up reductive algebraic group on the field.


Questions and Answers
  • 1. 
    Which is an example of a reductive group?
    • A. 

      Projective group

    • B. 

      Special linear group

    • C. 

      Abelian group

    • D. 

      Compact group

  • 2. 
    What is a configuration of vectors in an Euclidean space that satisfies certain geometrical properties?
    • A. 

      Root system

    • B. 

      Datum system

    • C. 

      Plane system

    • D. 

      Curve system

  • 3. 
    What is a maximal Zariski closed and connected solvable algebraic subgroup?
    • A. 

      Compact subgroup

    • B. 

      Projective subgroup

    • C. 

      Planar subgroup

    • D. 

      Borel subgroup

  • 4. 
    Which is an example of an algebraically closed field?
    • A. 

      Complex numbers

    • B. 

      Real numbers

    • C. 

      Rational numbers

    • D. 

      Irrational numbers

  • 5. 
    What is a non-constant polynomial that cannot be factored into the product of two non-constant polynomials?
    • A. 

      Reducible polynomial

    • B. 

      Irreducible polynomial

    • C. 

      Constant polynomial

    • D. 

      Projective polynomial

  • 6. 
    Which is a group that is an algebraic variety, such that the multiplication and inversion operations are given by regular maps on the variety?
    • A. 

      Compact group

    • B. 

      Lie group

    • C. 

      Algebraic group

    • D. 

      Planar group

  • 7. 
    What is a plane algebraic curve defined by an equation that is non-singular?  
    • A. 

      Elliptic curve

    • B. 

      Cubic curve

    • C. 

      Quadric curve

    • D. 

      Projective curve

  • 8. 
    What is a generalization of the general linear group which applies to Taylor polynomials instead of vectors at a point?
    • A. 

      Jet group

    • B. 

      Lie group

    • C. 

      Canort group

    • D. 

      Nilpotent group

  • 9. 
    What determines the irreducibility of a polynomial?
    • A. 

      Nature of coefficient

    • B. 

      Shape of slope

    • C. 

      Number of coefficient

    • D. 

      Nature of quotient

  • 10. 
    A univariate polynomial is absolutely irreducible if and only if its degree is what?
    • A. 

      Zero

    • B. 

      One

    • C. 

      Two

    • D. 

      Three

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