What Do You Know About Schur Algebras?

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What Do You Know About Schur Algebras? - Quiz

Schur algebras are useful in the field of representation theory under the science of structure, order, and relation otherwise known as mathematics.
They are specific limited-dimensional algebras intently connected with Schur–Weyl duality between general symmetric and linear groups.
To find out more about Schur algebras, take this short, intelligent quiz.


Questions and Answers
  • 1. 

    Schur algebras are named after who?

    • A.

      Isa Schur

    • B.

      Issai Schur

    • C.

      Issac Schur

    • D.

      Mathew Schur

    Correct Answer
    B. Issai Schur
    Explanation
    Schur algebras are named after Issai Schur, a mathematician who made significant contributions to the field of algebra. He introduced Schur algebras in his work on the representation theory of symmetric groups and proved fundamental theorems related to them. His work laid the foundation for the study of Schur algebras and their applications in various areas of mathematics.

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  • 2. 

    Who widely promoted the use of Schur algebras?

    • A.

      A. J. Green

    • B.

      J. A. Green

    • C.

      C. J. Green

    • D.

      J. C. Green

    Correct Answer
    B. J. A. Green
    Explanation
    J. A. Green widely promoted the use of Schur algebras.

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  • 3. 

    Schur algebras were used by which duo to prove finite generation of cohomology of finite group schemes? 

    • A.

      Friedlander and Suslin

    • B.

      Karin and Edman

    • C.

      Suslin and Edman

    • D.

      Friedlander and Karin

    Correct Answer
    A. Friedlander and Suslin
    Explanation
    Friedlander and Suslin used Schur algebras to prove the finite generation of cohomology of finite group schemes.

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  • 4. 

    Who put forth generalized Schur algebras?

    • A.

      Suslin

    • B.

      Donkin

    • C.

      Edman

    • D.

      Karin

    Correct Answer
    B. Donkin
    Explanation
    Donkin is the correct answer because he is the mathematician who put forth generalized Schur algebras. Suslin, Edman, and Karin are not associated with this concept.

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  • 5. 

    In which decade were generalised Schur algebras introduced?

    • A.

      1970s

    • B.

      1980s

    • C.

      1990s

    • D.

      2000s

    Correct Answer
    B. 1980s
    Explanation
    The correct answer is 1980s. Generalized Schur algebras were introduced in the 1980s.

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  • 6. 

    Which duo introduced quantized Schur algebras?

    • A.

      Suslin and James

    • B.

      Edward and Dipper

    • C.

      James and Karin

    • D.

      Dipper and James

    Correct Answer
    D. Dipper and James
    Explanation
    Dipper and James introduced quantized Schur algebras.

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  • 7. 

    Schur algebras have which global dimensions? 

    • A.

      Finite

    • B.

      Infinite

    • C.

      Semi-finite

    • D.

      Semi-infinite

    Correct Answer
    A. Finite
    Explanation
    Schur algebras have finite global dimensions. This means that the Schur algebras have a finite number of simple modules up to isomorphism. In other words, there are only finitely many irreducible representations of the Schur algebra.

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  • 8. 

    The name Schur algebra was because of who?

    • A.

      Suslin

    • B.

      Issai

    • C.

      Green

    • D.

      Karin

    Correct Answer
    C. Green
    Explanation
    The correct answer is Green. The name Schur algebra was given in honor of the mathematician Green.

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  • 9. 

    In which year was the monograph used to introduce Schur algebras published?

    • A.

      1978

    • B.

      1979

    • C.

      1980

    • D.

      1981

    • E.

      1982

    Correct Answer
    C. 1980
    Explanation
    The monograph used to introduce Schur algebras was published in 1980.

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  • 10. 

    In the modular case, Schur algebras were used by which duo to show that the problems of computing decomposition numbers for general linear groups and symmetric groups are actually equivalent?

    • A.

      Gordon James and Karin Erdmann

    • B.

      James Redman and Suslin Piers

    • C.

      Gordon James and Karin Redman

    • D.

      Michael Redman and Suslin Piers

    Correct Answer
    A. Gordon James and Karin Erdmann
    Explanation
    Gordon James and Karin Erdmann used Schur algebras to demonstrate that the problems of computing decomposition numbers for general linear groups and symmetric groups are equivalent in the modular case.

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  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
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    AdeKoju
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