Triple

Target class: decomposition in Lie theory
Context triple: [Iwasawa decomposition, instanceOf, decomposition in Lie theory]

• A. decomposition theorem
  The decomposition theorem is a fundamental result in algebraic geometry and topology stating that, under suitable conditions, the direct image of an intersection complex under a proper map splits as a direct sum of shifted semisimple perverse sheaves.
• B. concept in Lie theory chosen
  A concept in Lie theory is an abstract mathematical construct—such as a Lie group, Lie algebra, or representation—that captures continuous symmetries and their algebraic and geometric properties.
• C. basis in representation theory
  A basis in representation theory is a chosen set of vectors in a representation space such that every vector in the space can be uniquely expressed as a linear combination of them, allowing the linear operators representing group or algebra elements to be described concretely by matrices.
• D. result in representation theory
  A result in representation theory is a proven statement describing how algebraic structures, such as groups or algebras, can be represented by linear transformations on vector spaces and how these representations behave or decompose.
• E. subalgebra of a Lie algebra
  A subalgebra of a Lie algebra is a linear subspace that is closed under the Lie bracket, meaning the bracket of any two of its elements remains within the subspace.
• F. None of above.