What Do You Know About Schur Algebras?

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  • 1/10 Questions

    Schur algebras are named after who?

    • Isa Schur
    • Issai Schur
    • Issac Schur
    • Mathew Schur
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About This 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.

What Do You Know About Schur Algebras? - Quiz

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  • 2. 
    Who widely promoted the use of Schur algebras? - ProProfs

    Who widely promoted the use of Schur algebras?

    • A. J. Green

    • J. A. Green

    • C. J. Green

    • J. C. Green

    Correct Answer
    A. 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?  - ProProfs

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

    • Friedlander and Suslin

    • Karin and Edman

    • Suslin and Edman

    • 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? - ProProfs

    Who put forth generalized Schur algebras?

    • Suslin

    • Donkin

    • Edman

    • Karin

    Correct Answer
    A. 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? - ProProfs

    In which decade were generalised Schur algebras introduced?

    • 1970s

    • 1980s

    • 1990s

    • 2000s

    Correct Answer
    A. 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? - ProProfs

    Which duo introduced quantized Schur algebras?

    • Suslin and James

    • Edward and Dipper

    • James and Karin

    • Dipper and James

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

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  • 7. 
    Schur algebras have which global dimensions?  - ProProfs

    Schur algebras have which global dimensions? 

    • Finite

    • Infinite

    • Semi-finite

    • 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. 
    In which year was the monograph used to introduce Schur algebras published? - ProProfs

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

    • 1978

    • 1979

    • 1980

    • 1981

    • 1982

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

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  • 9. 
    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? - ProProfs

    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?

    • Gordon James and Karin Erdmann

    • James Redman and Suslin Piers

    • Gordon James and Karin Redman

    • 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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  • 10. 
    The name Schur algebra was because of who? - ProProfs

    The name Schur algebra was because of who?

    • Suslin

    • Issai

    • Green

    • Karin

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

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  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Jun 19, 2018
    Quiz Created by
    AdeKoju
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