2001/01/16 by Edwin Beggs, Edwin J. Beggs, Beggs, Edwin J.
Mathematics · Physics and Astronomy · #46L87 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Quantum Algebra (math.QA) #math.QA #msc:46L87
paper · pdf · doi:10.48550/arxiv.math/0101132
10 pages LaTeX
arxiv created 2001/01/16 · openalex publication_date 2001/01/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we extend the standard differential geometric theory of Hamiltonian dynamics to noncommutative spaces, beginning with symplectic forms. Derivations on the algebra are used instead of vector fields, and interior products and Lie derivatives with respect to derivations are discussed. Then the Poisson bracket of certain algebra elements can be defined by a choice of closed 2-form. Examples are given using the noncommutative torus, the Cuntz algebra, the algebra of matrices, and the algebra of matrix valued functions on \Bbb R2.