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
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