Definitions Flashcards

1
Q

Representation

A

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2
Q

Equivalent Representation

A

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3
Q

Faithful Representation

A

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4
Q

FG-Module

A

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5
Q

Endomorphism Relative To A Basis

A

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6
Q

Trivial FG-Module

A

.

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7
Q

Faithful FG-Module

A

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8
Q

Permutation Module

A

.

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9
Q

FG-Submodule

A

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10
Q

Irreducible FG-Module

A

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11
Q

Group Algebra

A

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12
Q

Regular FG-Module

A

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13
Q

Regular Representation

A

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14
Q

FG Acts On An FG-Module

A

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15
Q

FG-Homomorphism

A

.

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16
Q

Isomorphic FG-Modules

A

.

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17
Q

Direct Sum Of Vector Spaces

A

.

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18
Q

Projection

A

.

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19
Q

External Direct Sum Of Vector Spaces

A

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20
Q

External Direct Sum Of FG-Modules

A

.

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21
Q

Completely Irreducible FG-Module

A

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22
Q

Centre Of A Group Algebra

A

.

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23
Q

Centre Of A Group

A

.

24
Q

Composition Factor

A

.

25
Q

Common Composition Factor

A

.

26
Q

The Space Of CG-Homomorphisms

A

.

27
Q

Complete Set Of Non-Isomorphic Irreducible CG-Modules

A

.

28
Q

Group Acting On A Set

A

.

29
Q

Orbit

A

.

30
Q

Stabiliser

A

.

31
Q

Conjugacy Class

A

.

32
Q

Class Sums

A

.

33
Q

Trace

A

.

34
Q

Character Of A CG-Module

A

.

35
Q

Character Of A Representation

A

.

36
Q

Character Of A Group

A

.

37
Q

Irreducible/Reducible Character

A

.

38
Q

Degree Of A Character

A

.

39
Q

Linear Characters

A

.

40
Q

Trivial Character

A

.

41
Q

Kernal Of A Character

A

.

42
Q

Faithful Character

A

.

43
Q

Complex Conjugate Of A Character

A

.

44
Q

Regular Character

A

.

45
Q

Permutation Character

A

.

46
Q

Class Functions

A

.

47
Q

Inner Product On Set Of Functions From G To C

A

.

48
Q

External Direct Sum Of M Copies Of V

A

.

49
Q

Kronecker Delta Function

A

.

50
Q

Constituent

A

.

51
Q

Character Table

A

.

52
Q

Lift

A

.

53
Q

Commuter/Derived Subgroup

A

.

54
Q

mn-Dimensional Vector Space Over C

A

.

55
Q

Tensor Product Module

A

.

56
Q

Def 18.11

A

.

57
Q

Algebraic Integer

A

.