What Do You Know About Schur Algebras?

1) Which duo introduced quantized Schur algebras?

Suslin and James

Edward and Dipper

James and Karin

Dipper and James

Dipper and James introduced quantized Schur algebras.

Explanation

Dipper and James introduced quantized Schur algebras.

2) Schur algebras have which global dimensions?

Finite

Infinite

Semi-finite

Semi-infinite

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.

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.

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

1978

1979

1980

1981

1982

The monograph used to introduce Schur algebras was published in 1980.

Explanation

The monograph used to introduce Schur algebras was published in 1980.

4) 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

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.

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.

5) Schur algebras are named after who?

Isa Schur

Issai Schur

Issac Schur

Mathew Schur

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.

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.

6) Who widely promoted the use of Schur algebras?

A. J. Green

J. A. Green

C. J. Green

J. C. Green

J. A. Green widely promoted the use of Schur algebras.

Explanation

J. A. Green widely promoted the use of Schur algebras.

7) 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

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

Explanation

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

8) Who put forth generalized Schur algebras?

Suslin

Donkin

Edman

Karin

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.

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.