MATH380 index

A B C D G H I L M N O P Q R S T

A:

  • Algebra: Lec 3, Sec 2.2.
  • Algebraic integer: Lec 12, Sec 1.1.
  • Algebraic number: Lec 12, Sec 1.1.
  • Averaging idempotent: Lec 6, Sec 1.1.

    B:

  • Bilinear map: Lec 3, Sec 2.1.

    C:

  • Center of an algebra: Lec 8, Sec 1.1.
  • Character of a representation: Lec 1, Sec 3.
  • Class functions on a group (denoted by Gl(G)): Lec 1, Sec 3.
  • Commutator (in a group): Lec 5, Sec 1.1.
  • Complement(ary) subrepresentation: Lec 5, Sec 2.
  • Completely reducible representation: Lec 5, Sec 2.
  • Conjugate (of an algebraic number): Lec 12, Sec 1.1.

    D:

  • Derived subgroup: Lec 5, Sec 1.1.
  • Direct sum of representations: Lec 2, Sec 2.1.
  • Dual representation (of a group): Lec 4, Sec 2.2.

    G:

  • General linear group (denoted GL(V) or GL_n(F)): Lec 1, Sec 1.
  • Group algebra: Lec 3, Sec 3.2.

    H:

  • Homomorphism of representations: Lec 3, Sec 1.
  • Hom representation (of a group): Lec 4, Sec 2.2.

    I:

  • Induced representation: Lec 14, Sec 1.1.
  • Irreducible representation: Lec 1, Sec 2 and Lec 5, Sec 1.
  • Isomorphic representations: Lec 3, Sec 1.
  • Isomorphism of representations: Lec 3, Sec 1.

    I:

  • Left ideal: Lec 19, Sec 2.1.

    M:

  • Minimal polynomial: Lec 12, Sec 1.1.
  • Module over an associative (unital) algebra: Lec 3, Sec 2.3.
  • Multiplicity (of an irreducible representation): Lec 6, Sec 2.

    N:

  • Nilpotent ideal: Lec 23, Sec 1.1.

    O:

  • Opposite algebra: Lec 7, Sec 3.

    P:

  • Permutation representation (of a symmetric group): Lec 2, Sec 1.
  • Projector (to a subspace): Lec 6, Sec 1.2.
  • Proper subrepresentation: Lec 5, Sec 1.
  • Pullback of a representation: Lec 2, Sec 2.4.

    Q:

  • Quaternions: Lec 7, Sec 3.1.
  • Quotient representation: Lec 2, Sec 2.3.

    R:

  • Radical: Lec 23, Sec 1.1.
  • Regular representation (of a finite group): Lec 2, Sec 1.
  • Regular module (over an associative algebra): Lec 3, Sec 2.3.
  • Representation of a group: Lec 1, Sec 1.
  • Representation of an associative (unital) algebra: Lec 3, Sec 2.3.
  • Restriction of a representation: Lec 2, Sec 2.4
  • Right ideal: Lec 19, Sec 2.1.
  • Right module: Lec 19, Sec 2.1.

    S:

  • Semisimple algebras: Lec 19, Sec 1.2.
  • Sign representation (of a symmetric group): Lec 5, Sec 1.2.
  • Simple algebras: Lec 19, Sec 1.1.
  • Simple groups: Lec 1, Sec 4.
  • Skew-field (a.k.a. division ring): Lec 7, Sec 3.
  • Subrepresentation: Lec 2, Sec 2.2.
  • Symmetric polynomial: Lec 12, Sec 2.1.

    T:

  • Tensor monomials: Lec 4, Sec 1.1.
  • Tensor product of vector spaces: Lec 4, Sec 1.2.
  • Tensor product of representations of a group: Lec 4, Sec 2.1.
  • Trace form: Lec 23, Sec 1.2.
  • Trivial representation of a group: Lec 4, Sec 2.2.
  • Two-sided ideal: Lec 19, Sec 1.1.