MasterPVA and WAlg: Mathematica packages for Poisson vertex algebras and classical affine \mathcal W W -algebras

2016/03/31 by Matteo Casati, Daniele Valeri · 4 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Hamiltonian (control theory) #Homotopy and Cohomology in Algebraic Topology #Poisson distribution #Symbolic computation #Vertex (graph theory) #math-ph #math.MP #math.RA #math.RT #msc:17-08 #msc:17B08 #msc:17B63 #msc:17B69 #msc:17B80 #msc:37-04 #msc:37K30

paper · pdf · doi:10.1007/s40574-017-0146-9

published in Bollettino Della Unione Matematica Italiana 11(4), 503-531 (Springer Nature) · 29 pages, 31 figures. Revised structure and better title, improved the W(G2,f) example

arxiv created 2017/02/06 · openalex created_date 2017/06/30 · openalex publication_date 2017/12/09 · arxiv updated 2017/12/18 · openalex updated_date 2026/08/05

Abstract

We give an introduction to the Mathematica packages "MasterPVA" and "MasterPVAmulti used to compute lambda-brackets in Poisson vertex algebras, which play an important role in the theory of infinite-dimensional Hamiltonian systems. As an application, we give an introduction to the Mathematica package "WAlg" aimed to compute the lambda-brackets among the generators of classical affine W-algebras. The use of these packages is shown by providing some explicit examples.

Citations

• Lambda: A Mathematica package for operator product expansions in vertex algebras
• Classical Affine W-Algebras for \mathfrakgl_N and Associated Integrable Hamiltonian Hierarchies
• Poisson cohomology of scalar multidimensional Dubrovin–Novikov brackets
• A New Scheme of Integrability for (bi)Hamiltonian PDE