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
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