The Expansion star mod o (h(4)) and Computer-Assisted Proof Schemes in the Kontsevich Deformation Quantization

R. Buring*, A. V. Kiselev

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
32 Downloads (Pure)

Abstract

The Kontsevich deformation quantization combines Poisson dynamics, noncommutative geometry, number theory, and calculus of oriented graphs. To manage the algebra and differential calculus of series of weighted graphs, we present software modules: these allow generating the Kontsevich graphs, expanding the noncommutative & x22c6;-product by using a priori undetermined coefficients, and deriving linear relations between the weights of graphs. Throughout this text we illustrate the assembly of the Kontsevich & x22c6;-product up to order 4 in the deformation parameter Already at this stage, the & x22c6;-product involves hundreds of graphs; expressing all their coefficients via 149 weights of basic graphs (of which 67 weights are now known exactly), we express the remaining 82 weights in terms of only 10 parameters (more specifically, in terms of only 6 parameters modulo gauge-equivalence). Finally, we outline a scheme for computer-assisted proof of the associativity, modulo for the newly built & x22c6;-product expansion.

Original languageEnglish
Pages (from-to)701-754
Number of pages54
JournalExperimental Mathematics
Volume31
Issue number3
Early online date9-Nov-2019
DOIs
Publication statusPublished - 2022

Keywords

  • Associative algebra
  • noncommutative geometry
  • deformation quantization
  • Kontsevich graph complex
  • computer-assisted proof scheme
  • software module
  • template library
  • POISSON STRUCTURES

Cite this