How Well Do You Know Haagerup Property?
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.
- 1.
Which of these is irrelevant in this context?
- A.
T-menability
- B.
Set
- C.
Nonikov conjecture
- D.
Element
Correct Answer
B. SetExplanation
In this context, the term "set" is irrelevant because the question is asking about concepts or ideas related to "T-menability," "Nonikov conjecture," and "element." "Set" is a general term that does not specifically pertain to any of these concepts or ideas mentioned.Rate this question:
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- 2.
What is the other name for Haagerup property?
- A.
Gromorov property
- B.
Kazhdan property
- C.
T-menability
- D.
Gromorov T-menability
Correct Answer
D. Gromorov T-menability -
- 3.
What is the representation-theoretic form of rigidity?
- A.
Groups
- B.
Property
- C.
Set
- D.
Element
Correct Answer
B. PropertyExplanation
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.Rate this question:
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- 4.
Which if these does not engage the Haagerup property?
- A.
Operator
- B.
K-theory
- C.
Representation theory
- D.
Harmonic analysis
Correct Answer
A. OperatorExplanation
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."Rate this question:
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- 5.
Who invented the mathematical representation?
- A.
Agnes Alexandra
- B.
Uffe Haagerup
- C.
Van Andersen
- D.
Erikson Hansen
Correct Answer
B. Uffe HaagerupExplanation
Uffe Haagerup is credited with inventing the mathematical representation.Rate this question:
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- 6.
Which of these is not related to Haagerup property?
- A.
Baum-Connes conjecture
- B.
Nonikov conjecture
- C.
K-theory
- D.
Jensen theory
Correct Answer
D. Jensen theoryExplanation
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.Rate this question:
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- 7.
Which of these groups is not with Haagerup property?
- A.
Coxeter groups
- B.
Amenable groups
- C.
Compact groups
- D.
Hilbert groups
Correct Answer
D. Hilbert groupsExplanation
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.Rate this question:
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- 8.
What is the group with presentation called?
- A.
Coxeter group
- B.
Symmetry group
- C.
Polyhedra
- D.
Involition
Correct Answer
A. Coxeter groupExplanation
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.Rate this question:
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- 9.
How many geometric groups have Haagerup property?
- A.
7 groups
- B.
8 groups
- C.
10 groups
- D.
4 groups
Correct Answer
A. 7 groupsExplanation
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.Rate this question:
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- 10.
What year saw the Nonikov conjecture publicised?
- A.
1965
- B.
1961
- C.
1973
- D.
1979
Correct Answer
A. 1965Explanation
The Nonikov conjecture was publicized in 1965.Rate this question:
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Mar 22, 2023Quiz Edited by
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Jul 18, 2018Quiz Created by
Hanero
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