1.
Which of these is irrelevant in this context?
Correct Answer
B. Set
Explanation
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.
2.
What is the other name for Haagerup property?
Correct Answer
D. Gromorov T-menability
3.
What is the representation-theoretic form of rigidity?
Correct Answer
B. 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.
4.
Which if these does not engage the Haagerup property?
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."
5.
Who invented the mathematical representation?
Correct Answer
B. Uffe Haagerup
Explanation
Uffe Haagerup is credited with inventing the mathematical representation.
6.
Which of these is not related to Haagerup property?
Correct Answer
D. 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.
7.
Which of these groups is not with Haagerup property?
Correct Answer
D. 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.
8.
What is the group with presentation called?
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.
9.
How many geometric groups have Haagerup property?
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.
10.
What year saw the Nonikov conjecture publicised?
Correct Answer
A. 1965
Explanation
The Nonikov conjecture was publicized in 1965.