How Well Do You Know Haagerup Property?

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1/10 Questions

Which of these is irrelevant in this context?
- T-menability
- Set
- Nonikov conjecture
- Element

About This Quiz

Haagerup property is named after Uffe Haagerup and it can be considered a property of groups that strongly negates Kazhdan's property (T). The Haagerup property is common in a lot of mathematical fields.
This includes harmonic analysis, representation theory, operator K-theory, geometric group theory. We hope you have the necessary base to answer a few questions.

How Well Do You Know Haagerup Property? - Quiz

2.

What is the other name for Haagerup property?
- Gromorov property
- Kazhdan property
- T-menability
- Gromorov T-menability
Correct Answer

A. Gromorov T-menability
3.

What is the representation-theoretic form of rigidity?
- Groups
- Property
- Set
- Element
Correct Answer

A. Property

Explanation

In representation theory, rigidity refers to the property of a representation that cannot be deformed or changed. It means that the representation is fixed or rigid in its structure. Therefore, the representation-theoretic form of rigidity is a property, as it describes the fixed nature of the representation.

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4.

Which if these does not engage the Haagerup property?
- Operator
- K-theory
- Representation theory
- Harmonic analysis
Correct Answer

A. Operator

Explanation

The Haagerup property is a property in operator theory that is related to the existence of certain types of bounded linear operators. Operator theory is the study of linear operators on a given function space, so it is directly related to the Haagerup property. On the other hand, K-theory, representation theory, and harmonic analysis are all mathematical fields that are related to the study of functions and operators, but they do not directly deal with the Haagerup property. Therefore, the correct answer is "Operator."

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5.

Who invented the mathematical representation?
- Agnes Alexandra
- Uffe Haagerup
- Van Andersen
- Erikson Hansen
Correct Answer

A. Uffe Haagerup

Explanation

Uffe Haagerup is credited with inventing the mathematical representation.

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6.

Which of these is not related to Haagerup property?
- Baum-Connes conjecture
- Nonikov conjecture
- K-theory
- Jensen theory
Correct Answer

A. Jensen theory

Explanation

The Haagerup property is a property in operator algebra theory that characterizes certain groups and C*-algebras. The Baum-Connes conjecture and Nonikov conjecture are both related to the Haagerup property and have been extensively studied in this context. K-theory is also closely related to the Haagerup property, as it provides a framework for studying the algebraic and topological properties of C*-algebras. However, Jensen theory is not directly related to the Haagerup property and is a different area of mathematics altogether.

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7.

Which of these groups is not with Haagerup property?
- Coxeter groups
- Amenable groups
- Compact groups
- Hilbert groups
Correct Answer

A. Hilbert groups

Explanation

The Haagerup property is a property in operator algebras that is related to the existence of certain types of positive definite functions. Coxeter groups, amenable groups, and compact groups are all known to have the Haagerup property. However, Hilbert groups, which are infinite-dimensional generalizations of the Heisenberg group, do not have the Haagerup property.

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8.

What is the group with presentation called?
- Coxeter group
- Symmetry group
- Polyhedra
- Involition
Correct Answer

A. Coxeter group

Explanation

A Coxeter group is a mathematical group that is defined by a set of generators and relations. It is named after H.S.M. Coxeter, who extensively studied these groups. Coxeter groups have applications in various areas of mathematics, including geometry and combinatorics. They are particularly useful in the study of symmetry, as they can be used to describe the symmetries of regular polytopes and other geometric objects. Therefore, Coxeter group is the correct answer for the group with presentation.

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9.

How many geometric groups have Haagerup property?
- 7 groups
- 8 groups
- 10 groups
- 4 groups
Correct Answer

A. 7 groups

Explanation

The Haagerup property is a property of certain geometric groups, which are groups that can be defined by a geometric structure. The question asks how many geometric groups have the Haagerup property. The correct answer is 7 groups, indicating that there are 7 known geometric groups that have been proven to have the Haagerup property.

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10.

What year saw the Nonikov conjecture publicised?
- 1965
- 1961
- 1973
- 1979
Correct Answer

A. 1965

Explanation

The Nonikov conjecture was publicized in 1965.

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