# How Much Do You Know About Affine Lie Algebra?

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Anouchka
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Questions: 10 | Attempts: 130  Settings  Lie Algebra is possibly another branch of algebra, which is difficult to define or explain. But those who know about it define it as an infinite-dimensional Lie algebra constructed in a canonical fashion out of a finite-dimensional simple Lie algebra. So, how much do you know about this discipline? Take our quiz and find out.

• 1.

### How many meaning does the Cartan matrix have?

• A.

3

• B.

2

• C.

5

• D.

6

A. 3
Explanation
The Cartan matrix has three different meanings or interpretations. It can represent the structure of a semisimple Lie algebra, the intersection form on the root lattice, and the Gram matrix of the inner product on the weight lattice. Each of these interpretations provides valuable information about the algebraic structure being studied.

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• 2.

### What's the string theory?

• A.

It's the theoretical framework in which the point-like particles of particle are replaced by two-dimensional objects called strings.

• B.

It's the theoretical framework in which the point-like particles of particle are replaced by three-dimensional objects called strings.

• C.

It's the theoretical framework in which the point-like particles of particle are replaced by five-dimensional objects called strings.

• D.

It's the theoretical framework in which the point-like particles of particle are replaced by one-dimensional objects called strings.

D. It's the theoretical framework in which the point-like particles of particle are replaced by one-dimensional objects called strings.
Explanation
The string theory is a theoretical framework that replaces point-like particles with one-dimensional objects called strings. This theory suggests that these strings vibrate at different frequencies, giving rise to different particles and forces in the universe.

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• 3.

### What are loop algebras?

• A.

They are certain types of Lie algebras, of particular interest in theoretical mathematics.

• B.

They are certain types of Lie physics, of particular interest in theoretical algebras.

• C.

They are certain types of Lie algebras, of particular interest in theoretical physics.

• D.

They are certain types of algebras, of particular interest in theoretical mathematics.

C. They are certain types of Lie algebras, of particular interest in theoretical physics.
Explanation
Loop algebras are a specific type of Lie algebras that are of special importance in theoretical physics. These algebras have applications in various areas of physics, such as string theory and quantum field theory. They are used to describe symmetries and transformations in these theories, providing a mathematical framework to study physical phenomena. Therefore, loop algebras are of particular interest in theoretical physics rather than mathematics or any other field mentioned in the options.

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• 4.

### What's the other term for quantum anomaly?

• A.

Quantums

• B.

Decimals

• C.

Whole numbers

• D.

Anomaly

D. Anomaly
Explanation
The term "quantum anomaly" refers to an abnormality or deviation from the expected behavior in the field of quantum mechanics. It is a specific type of anomaly that occurs at the quantum level. Therefore, the correct answer is "Anomaly."

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• 5.

### What's an automorphism?

• A.

It's an isomorphism from a mathematical object to itself.

• B.

It's an isomorphic from a mathematical object to itself.

• C.

It's an metamorphism from a mathematical object to itself.

• D.

It's an sophism from a mathematical object to itself.

A. It's an isomorphism from a mathematical object to itself.
Explanation
An automorphism is a type of isomorphism where a mathematical object is mapped onto itself. Isomorphisms preserve the structure and properties of the objects they map, so an automorphism is a special case where the object is mapped onto itself. This means that the object remains unchanged under the automorphism, maintaining its original properties and relationships.

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• 6.

### What's a Dynkin diagram?

• A.

It's a type of graph with some edges.

• B.

It's a type of graph with some edges doubled or tripled.

• C.

It's a type of graph with some doubled edges.

• D.

It's a type of graph with some tripled edges.

B. It's a type of graph with some edges doubled or tripled.
Explanation
A Dynkin diagram is a type of graph that represents the root system of a Lie algebra. The edges in the diagram correspond to the roots, which are the fundamental elements of the algebra. In a Dynkin diagram, some edges can be doubled or tripled to indicate certain properties of the root system. This doubling or tripling of edges represents specific relationships between the roots and provides important information about the structure of the Lie algebra.

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• 7.

### What's a group extension in mathematics?

• A.

It's a general means of describing a group in terms of a particular normal group and quotient group.

• B.

It's a general means of describing a group in terms of a particular normal group and quotient subgroup.

• C.

It's a general means of describing a group in terms of a particular normal subgroup and quotient group.

• D.

It's a general means of describing a normal subgroup and quotient group.

C. It's a general means of describing a group in terms of a particular normal subgroup and quotient group.
Explanation
A group extension in mathematics is a general means of describing a group by specifying a particular normal subgroup and quotient group. This allows for a more detailed understanding of the group structure and the relationships between its subgroups. By identifying the normal subgroup and quotient group, we can gain insight into the group's properties and study its behavior in a more systematic way.

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• 8.

### What's the other term for Laurent polynomials?

• A.

Laurent series

• B.

Grant series

• C.

Grant numbers

• D.

Grant algebra

A. Laurent series
Explanation
Laurent polynomials are also known as Laurent series.

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• 9.

### What's a lining form?

• A.

It's a symmetric linear form that plays a basic role in the theories of Lie groups and Lie algebras.

• B.

It's a symmetric tri linear form that plays a basic role in the theories of Lie groups and Lie algebras.

• C.

It's a symmetric bi linear form that plays a basic role in the theories of Lie groups and and shapes.

• D.

It's a symmetric bi linear form that plays a basic role in the theories of Lie groups and Lie algebras.

D. It's a symmetric bi linear form that plays a basic role in the theories of Lie groups and Lie algebras.
Explanation
A lining form is a symmetric bi-linear form that is important in the study of Lie groups and Lie algebras. This type of form is used to define the structure and properties of these mathematical objects. It is symmetric, meaning that it is invariant under the exchange of its two arguments, and bi-linear, meaning that it is linear in each argument separately. This form is fundamental in understanding the relationships and interactions within Lie groups and Lie algebras.

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• 10.

### What's a semidirect product?

• A.

It's a generalization of a direct product.

• B.

It's a generalization of a indirect product.

• C.

It's a generalization of a direct function.

• D.

It's a generalization of a curve. Back to top