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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