Linear Algebra

• Comparable subspaces
• Compatibility of a basis with a subspace
• Chain of subspaces, filtration of a vector space.
• Modular law
• Exact sequences
• Internal and external direct sums of vector spaces
• Linear relations

Quivers

• Quiver: vertices, arrows, tail, head
• Underlying graph of a quiver
• Loop (an arrow α with h(α) = t(α))
• Connected quivers
• sink, source

Special quivers

• Quivers of type A_n
  The linearly oriented quiver of type A_n
• Quivers obtained from a subquiver by attaching an arm
• Tree quivers
• Star quivers
• the 3-subspace quiver
• Kronecker quiver

Representations of quivers

• Representation of a quiver, zero representation, support of the representation.
• Direct sum decomposition, indecomposable representaation
• Homomorphism f : M → M' between representations of a quiver
  Monomorphism, epimorphism, isomorphism
• Addition and scalar multiplication for homomorphisms
• Composition of homomorphisms
• Subrepresentation, Factor representation
• Kernel, image, cokernel of a homomorphism
• Thin representation
• Representation, decreasing on an arm
• the simple representation S(x)
• y-reduced representations

The reflection functors σ_y⁺ and σ_y^-