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PBWDeformations

Introduction

The package PBWDeformations will provide both a general framework and specialized functions in order to

  • classify PBW deformations of certain smash products and
  • study their representations.

To solve classification problems efficiently, we use representation theoretic ideas.

Features

  • Construct Lie algebras and their modules.
  • Construct smash products of the form $TV \rtimes U(L)$ for a Lie algbra $L$ and a module $V$.
  • Construct deformations of such smash products.
  • Compute a normal form for elements of smash products and their deformations.
  • Check, if a given deformation is a PBW-deformation (using [WW14]).
  • For some smash product, compute a basis of all PBW-deformations up to a given degree (using [WW14]). It is possible to give a basis of the relevant part of the deformation space, which is then used in the computation.
  • For some modules of $\mathfrak{so}_n$, give an explicit basis using arc diagrams or pseudographs (cf. [FM22]).

Installation

As this package heavily relies on Oscar, it is recommended to install Oscar first (installation instructions). Then, install this package via the Julia package manager:

] add PBWDeformations

Outline

Index