Differential Calculi of Poincare-Birkhoff-Witt type on Universal Enveloping Algebras

1995/06/09 by R. Martini, Martini, R., Gerhard F. Post +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.q-alg/9506010

openalex publication_date 1995/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Differential calculi of Poincare-Birkhoff-Witt type on universal enveloping algebras of Lie algebras g are defined. This definition turns out to be independent of the basis chosen in g. The role of automorphisms of g is explained. It is proved that no differential calculus of Poincare-Birkhoff-Witt type exists on semi-simple Lie algebras. Examples are given, namely gl_n, Abelian Lie algebras, the Heisenberg algebra, the Witt and the Virasoro algebra. Completely treated are the 2-dimensional solvable Lie algebra, and the 3-dimensional Heisenberg algebra.

Citations

• Differential calculus on compact matrix pseudogroups (quantum groups)

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