Index 227

Manifold, 25

Maschke’s theorem, 59

Maximal ideal, 15

McKay graph, 149

Minimal polynomial, 95

Module of finite length, 53

Monoidal category, 179

Morita equivalence, 215

Morita equivalent rings, 187

Morphism of complexes, 188

Natural transformation, 181

Orthogonality of characters, 65

Orthogonality of matrix elements,

70

Partition, 110

Path algebra of a quiver, 20

Polynomial representation, 130

Positive root, 162

Progenerator, 214

Projective cover, 210

Projective dimension of a module,

212

Projective generator, 214

Projective module, 202, 203

Projective object, 203

Projective resolution, 204

Pure tensor, 31

q-Weyl algebra, 17, 18

Quasi-inverse functor, 183

Quaternion algebra, 83

Quaternion group, 63

Quaternions, 83

Quiver, 7, 19

Quiver of finite type, 7, 148

Quotient algebra, 15

Quotient representation, 15

Radical, 46

Rational representation, 130

Reflection functor, 164

Regular representation, 10

Representable functor, 183

Representation, 5, 10

Representation of a group, 59

Representation of a Lie algebra, 24

Representation of a quiver, 7, 19

Representation of complex type, 91

Representation of quaternionic

type, 91

Representation of real type, 91

Representations of the symmetric

group, 110

Restriction of a representation, 105

Right adjoint functor, 184

Right exact functor, 191

Right ideal, 15

Right module, 10

Root, 161

Schur functor, 180

Schur polynomials, 128

Schur’s lemma, 11

Schur-Weyl duality, 119, 122

Semidirect product, 142

Semisimple abelian category, 191

Semisimple algebra, 48

Semisimple representation, 41

Shearing modulus, 86

Short exact sequence, 188

Simple algebra, 15

Simple reflection, 163

Simple representation (module), 10

Simple root, 161

Sink, 164

Solvable group, 98

Solvable Lie algebra, 39

Source, 164

Specht module, 111

Split short exact sequence, 188

Stress tensor, 85

Subrepresentation, 5, 10

Sum of squares formula, 60

Sylvester criterion, 147

Symmetric algebra, 35

Symmetric power, 33

Tensor algebra, 35

Tensor product of linear maps, 32

Tensor product of representations

of a Lie algebra, 37

Tensor product of vector spaces, 31

Tensors of type (m, n), 31

Tor functor, 203