Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Poincaré–Birkhoff–Witt basis | Statement: [universal enveloping algebra, hasBasisDescribedBy, Poincaré–Birkhoff–Witt basis]

Target entity: Poincaré–Birkhoff–Witt basis
Context triple: [universal enveloping algebra, hasBasisDescribedBy, Poincaré–Birkhoff–Witt basis]

• A. The Poincaré-Birkhoff-Witt theorem in ring theory chosen
  "The Poincaré-Birkhoff-Witt theorem in ring theory" is a mathematical work, attributed here to N. G. de Bruijn, that studies and applies the Poincaré–Birkhoff–Witt theorem in the context of associative and Lie-theoretic ring structures.
• B. Bott–Samelson theorem
  The Bott–Samelson theorem is a fundamental result in algebraic topology and geometry that provides a resolution of singularities for Schubert varieties via Bott–Samelson varieties, illuminating the topology and cohomology of flag manifolds.
• C. Gelfand–Tsetlin basis
  The Gelfand–Tsetlin basis is a canonical, combinatorially defined basis for representations of certain Lie algebras and groups, particularly used in the representation theory of GL(n) and related structures.
• D. Beilinson–Bernstein localization theorem
  The Beilinson–Bernstein localization theorem is a fundamental result in geometric representation theory that realizes representations of semisimple Lie algebras as sheaves of differential operators on flag varieties, establishing an equivalence between algebraic and geometric categories.
• E. Rota–Baxter algebra
  A Rota–Baxter algebra is an associative algebra equipped with a linear operator satisfying a specific integration-like identity that generalizes the properties of integral and summation operators in algebraic form.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasBasisDescribedBy
Context triple: [universal enveloping algebra, hasBasisDescribedBy, Poincaré–Birkhoff–Witt basis]

• A. hasBasisIn
  Indicates that one entity is founded, derived, or justified on the grounds of another entity.
• B. hasStandardBasis
  Indicates that a given vector space is equipped with or possesses its usual canonical set of basis vectors.
• C. hasCanonicalBasis chosen
  Indicates that there exists a standard or preferred basis associated with an entity, typically used as the reference basis in its context.
• D. proposedRepresentationBasis
  Indicates that one entity has been put forward as the foundational or reference basis for representing or encoding another entity.
• E. hasGivenNameBasis
  Indicates that one entity’s given name is derived from, based on, or formed using another entity (such as a name, word, or person) as its basis.
• F. None of above.