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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