Which of these has been an advantage of the representation of Hecke Algebra?

Dissociation of nuclear formular

Hecke Algebra Trivia Quiz

Reviewed by Editorial Team

The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.

Learn about Our Editorial Process

| By Gregorynaomi

Gregorynaomi

Community Contributor

Quizzes Created: 1462 | Total Attempts: 864,211

| Attempts: 150

Quiz Flashcard

Questions

Feedback

During the Quiz End of Quiz

Difficulty

Sequential Easy First Hard First

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

1/10 Questions

What can Hecke Algebra be interpreted as?
- Coxeter
- Algebra of double cosets
- Effective Factorisation
- Algebra of co-inhibition

About This Quiz

Hecke algebra in mathematics refers to a certain class of algebra related to the approach of Erich Hecke a German mathematician. Hecke Algebra can be interpreted as an algebra of double cosets. Are you familiar with this topic? Try this quiz.

2.

Which of these is a deformation of coxeter groups?
- Double Cosets Algebra
- Hecke cosets
- Iwahori-Hecke Algebra
- Hecke Algebra
Correct Answer

A. Iwahori-Hecke Algebra

Explanation

The Iwahori-Hecke Algebra is a deformation of the Hecke Algebra, which in turn is a deformation of the group algebra of the symmetric group, also known as the Coxeter group. Deformation refers to a mathematical process of modifying a structure while preserving certain properties. In this case, the Iwahori-Hecke Algebra is a modified version of the Hecke Algebra, designed to study representations of certain groups called Iwahori-Hecke algebras. Therefore, the Iwahori-Hecke Algebra is a deformation of Coxeter groups.

Rate this question:
3.

Hecke Algebra are quotient of which type of ring?
- Endomorphism
- Auslander
- Artin Braid group
- Reiten
Correct Answer

A. Artin Braid group

Explanation

The Hecke Algebra is a quotient of the Artin Braid group. The Artin Braid group is a mathematical structure that represents the ways in which strands can be braided together. The Hecke Algebra, on the other hand, is a generalization of the symmetric group algebra that arises in the study of representations of finite groups. The connection between the two lies in the fact that the Hecke Algebra can be obtained by quotienting the group algebra of the Artin Braid group by certain relations. Therefore, the correct answer is Artin Braid group.

Rate this question:
4.

In Hecke Algebra of coxeter group, what does R have?
- Isomorphic variable
- Identity
- Ring
- Valency
Correct Answer

A. Identity

Explanation

In the Hecke Algebra of a Coxeter group, the element R refers to the identity element. This means that when R is multiplied with any other element in the algebra, it does not change the value of that element. The identity element is an important concept in algebra as it serves as the neutral element for multiplication.

Rate this question:
5.

The element of natural basis is which of the following?
- Multiplicative
- Additive
- Inverse
- Coherent
Correct Answer

A. Multiplicative

Explanation

The element of natural basis is multiplicative because a natural basis is a set of vectors that spans a vector space and can be used to express any vector in that space as a linear combination of the basis vectors. In this context, the term "multiplicative" refers to the fact that the basis vectors are combined using multiplication, rather than addition or any other operation.

Rate this question:
6.

Who discovered the quantum groups?
- Hecke
- Lamar Jumbo
- Eric Iwahori
- Michio Jimbo
Correct Answer

A. Michio Jimbo

Explanation

Michio Jimbo is credited with the discovery of quantum groups. Quantum groups are a mathematical concept that emerged in the 1980s as an extension of the theory of Lie groups. They have applications in various areas of mathematics and physics, including representation theory, knot theory, and statistical mechanics. Jimbo's work on quantum groups has had a significant impact on the field and has led to further developments and applications in the years since its discovery.

Rate this question:
7.

How many relation does the multiparameter Hecke Algebra have?
- 3
- 4
- 2
- Infinite
Correct Answer

A. 2

Explanation

The multiparameter Hecke Algebra has 2 relations.

Rate this question:
8.

Who proposed Hecke Algebra to be the foundation of Topological Quantum computation?
- Jon Bakery
- Mike Fred
- Michael Freedman
- Iwahori
Correct Answer

A. Michael Freedman

Explanation

Michael Freedman proposed Hecke Algebra to be the foundation of Topological Quantum computation.

Rate this question:
9.

What does R stand for in Hecke Algebra of a coxeter group?
- Cummulative Ring
- Associative ring
- Artinian Ring
- Commutative ring
Correct Answer

A. Commutative ring

Explanation

The correct answer is "Commutative ring." In the Hecke Algebra of a Coxeter group, the letter R stands for "Commutative ring." This means that the algebraic structure associated with the Coxeter group is a commutative ring, where multiplication is commutative and satisfies certain properties. This is an important property in the study of Coxeter groups and their associated algebras.

Rate this question:
10.

Which of these has been an advantage of the representation of Hecke Algebra?
- Discovery of Quantum groups
- Dissociation of nuclear formular
- Discovery of Artinian Rings
- Increase in algebra scope
Correct Answer

A. Discovery of Quantum groups

Explanation

The representation of Hecke Algebra has been advantageous in the discovery of Quantum groups. This is because Hecke Algebras, which are a type of algebraic structure, have been used to study and understand the properties of Quantum groups. Quantum groups are a generalization of Lie groups and Lie algebras, and they have important applications in various areas of mathematics and physics, such as quantum mechanics and theoretical physics. Therefore, the representation of Hecke Algebra has played a significant role in the advancement and exploration of Quantum groups.

Rate this question:

1