Index

Abelian category, 186

Acyclic complex, 188

Additive functor, 190

Adjacency matrix, 146

Adjoint functors, 184

Ado’s theorem, 22

Aﬃne Dynkin diagram, 148

Algebra of dual numbers, 55

Algebra of endomorphisms of a

vector space, 9

Algebra of polynomials, 9

Algebraic conjugate, 95

Algebraic integer, 93

Algebraic number, 93

Algebraic representation, 130

Algebras defined by generators and

relations, 16

Artin’s theorem, 141

Associative algebra, 5, 9

Basic algebra, 216

Block, 213

Burnside’s theorem, 98

Cartan matrix, 160

Cartan matrix of a finite

dimensional algebra, 212

Casimir operator, 38

Category, 178

Central character, 14

Central function, 61

Character group, 62

Character of a group

representation, 61

Character of a representation, 48

Character table, 71

Class function, 61

Clifford algebra, 55

Coboundary, 188

Cocycle, 54, 188

Cohomology, 187

Cohomology class, 188

Commutant of a Lie algebra, 39

Commutative algebra, 9

Companion matrix, 94

Complete system of orthogonal

idempotents, 210

Completely reducible

representation, 41

Complex, 187

Complex conjugate representation,

69

Compression modulus, 86

Connecting homomorphism, 189

Content of a Young diagram, 118

Coxeter element, 169

Coxeter functor, 164

Cyclic quiver, 173

Cyclic representation, 16

Cyclic vector, 16

225