What Do You Know About The Root Datum?
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.
- 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
Questions: 12 | Attempts: 5566199 | Last updated: Mar 22, 2022
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