# How Much Do You Know About Restricted Representation

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In mathematics, there's a thing called restricted representation. It is described as the construction in the representation of groups. In other words, these representations supposedly form a representation of a whole group. So, what do you know about this theory? Try our quiz and see if you have enough knowledge to successfully complete it.

• 1.

### What's explicit symmetry breaking?

• A.

It's the breaking of a symmetry of a theory by terms in its defining equations of motion that do not respect the symmetry.

• B.

It's the breaking of a shape by terms in its defining equations of motion that do not respect the symmetry.

• C.

It's the breaking of a symmetry of a theory by terms in its defining equations of motion that do not respect the theory.

• D.

It's the breaking of a symmetry of a calculations by terms in its defining equations of motion that do not respect the symmetry.

A. It's the breaking of a symmetry of a theory by terms in its defining equations of motion that do not respect the symmetry.
Explanation
Explicit symmetry breaking refers to the breaking of a symmetry in a theory. This occurs when the defining equations of motion in the theory include terms that do not respect the symmetry. In other words, the equations of motion introduce terms that violate the symmetry that the theory originally possessed. This breaking of symmetry can have significant implications for the behavior and predictions of the theory.

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• 2.

### What's a symmetry group?

• A.

It's the group of all transformation under which the object is variant.

• B.

It's the group of all transformation under which the object is invariant with composition as the group operation

• C.

It's the group of all transformation under which the object is variant with composition as the group operation

• D.

It's all transformations under which the object is invariant with composition as the group operation

B. It's the group of all transformation under which the object is invariant with composition as the group operation
Explanation
The correct answer is "It's the group of all transformation under which the object is invariant with composition as the group operation". This means that a symmetry group consists of all the transformations that can be applied to an object without changing its overall shape or structure, and the composition of these transformations is the group operation. In other words, the symmetry group is the set of all transformations that preserve the object's symmetry.

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• 3.

### What's quantum mechanics?

• A.

It's the theory in physics which describes plants at the smallest scales of energy .

• B.

It's the fundamental theory in biology which describes nature at the smallest scales of energy .

• C.

It's the fundamental theory in physics which describes nature at the smallest scales of energy .

• D.

It's the fundamental theory in mathematics which describes nature at the smallest scales of energy .

C. It's the fundamental theory in physics which describes nature at the smallest scales of energy .
Explanation
Quantum mechanics is the fundamental theory in physics that describes nature at the smallest scales of energy. It deals with the behavior of particles and energy at the quantum level, where traditional Newtonian physics no longer applies. This theory has been successful in explaining various phenomena such as the behavior of atoms, molecules, and subatomic particles. It has also led to the development of technologies such as lasers, transistors, and quantum computing.

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• 4.

### What's Frobenius reciprocity?

• A.

It's a theorem expressing a duality between the process of adding and inducing.

• B.

It's a theorem expressing a duality between the process of restricting and cutting.

• C.

It's a theorem expressing a duality between the process of restricting and changing.

• D.

It's a theorem expressing a duality between the process of restricting and inducing.

D. It's a theorem expressing a duality between the process of restricting and inducing.
Explanation
Frobenius reciprocity is a theorem that establishes a duality between the process of restricting and inducing. It states that when a representation of a subgroup is restricted to a smaller subgroup, and then induced back to the original group, it is isomorphic to the original representation. This theorem allows for the study of representations of a group through the study of representations of its subgroups, providing a useful tool in representation theory.

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• 5.

### What's the Stark effect?

• A.

It's the shifting and splitting of spectral lines of atoms and molecules due to presence of an external electric field.

• B.

It's the splitting of spectral lines of atoms and molecules due to presence of an external electric field.

• C.

It's the shifting of spectral lines of atoms and molecules due to presence of an external electric field.

• D.

It's the shifting and splitting of lines of molecules due to presence of an external electric field.

A. It's the shifting and splitting of spectral lines of atoms and molecules due to presence of an external electric field.
Explanation
The Stark effect refers to the shifting and splitting of spectral lines of atoms and molecules when an external electric field is applied. This phenomenon occurs due to the interaction between the electric field and the charged particles in the atoms or molecules. The electric field causes the energy levels of the particles to shift, resulting in the spectral lines being shifted or split. This effect is important in the study of atomic and molecular spectroscopy and provides valuable information about the structure and behavior of these particles in the presence of electric fields.

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• 6.

### What does the Clifford theory do?

• A.

It describes the relation between representation of a normal subgroup.

• B.

It describes the relation between a group and those of a normal subgroup.

• C.

It describes the relation between representation of a group and those of a normal subgroup.

• D.

It describes the relation between representation of a group and those of a normal different group.

C. It describes the relation between representation of a group and those of a normal subgroup.
Explanation
The Clifford theory describes the relationship between the representation of a group and the representation of a normal subgroup. It provides insights into how the representations of the subgroup relate to the representations of the whole group.

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• 7.

### What's group homomorphism?

• A.

It's from the function h:G----H such that for all U and V in G it holds that H(u*v)=h(v)

• B.

It's from the function h:G----H such that for all V in G it holds that H(u*v)=h(u).h(v)

• C.

It's from the function h:G----H such that for all U and V in G it holds that H(u*v)=h(u).h(v)

• D.

It's from the function h:G----H

C. It's from the function h:G----H such that for all U and V in G it holds that H(u*v)=h(u).h(v)
Explanation
The correct answer is "It's from the function h:G----H such that for all U and V in G it holds that H(u*v)=h(u).h(v)". This answer accurately describes group homomorphism by stating that the function h maps elements from group G to group H in a way that preserves the group operation. It specifies that for any elements U and V in G, the product of their images under h in H is equal to the image of their product under h.

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• 8.

### What is ring mathematics?

• A.

It's a fundamental algebraic structure used in abstract algebraic

• B.

It's a fundamental algebraic structure used in geometry

• C.

It's a fundamental algebraic structure used in biology

• D.

It's a fundamental algebraic structure used in physics

A. It's a fundamental algebraic structure used in abstract algebraic
Explanation
Ring mathematics is a fundamental algebraic structure used in abstract algebraic. Rings are sets equipped with two binary operations, addition and multiplication, which satisfy certain properties. They are used to study various mathematical concepts such as number systems, polynomials, and matrices. Rings provide a framework for understanding algebraic structures and their properties, making them essential in abstract algebraic.

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• 9.

### What's a vector space?

• A.

It's a collection of objects called functions.

• B.

It's a collection of objects called identities.

• C.

It's a collection of objects called vectors.

• D.

It's a collection of objects called algebras.

C. It's a collection of objects called vectors.
Explanation
A vector space is a mathematical structure that consists of a collection of objects called vectors. These vectors can be added together and multiplied by scalars, satisfying certain properties such as closure under addition and scalar multiplication. The concept of a vector space is fundamental in linear algebra and has applications in various areas of mathematics and physics.

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• 10.

### What are quaternions?

• A.

They are a number system that extends the complex number.

• B.

They are a number system that extends the simple number.

• C.

They are a number system that extends a function

• D.

They are a number system that extends a mathematical identity.

A. They are a number system that extends the complex number.
Explanation
Quaternions are a number system that extends the complex numbers. While complex numbers are made up of a real part and an imaginary part, quaternions have four components: a real part and three imaginary parts. This extension allows for more complex calculations and is often used in computer graphics, robotics, and physics.

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