SuperLie

SuperLie: A Mathematica package for calculations in Lie algebras and superalgebras. SuperLie is a Mathematica-based package designed for solutions of scientific and computational problems related to Lie algebras and Lie superalgebras, their q-deformations included. Using SuperLie one can construct objects habitual for the mathematician (vector spaces and superspaces, algebras and modules over these algebras) in a way (hopefully) accessible to the engineer. SuperLie can solve various applied problems and theoretical problems of considerable importance to the physicists. In particular, SuperLie allows one to perform calculations and symbolic transformations in order to determine generators and relation of Lie (super)algebrass, vacuum vectors (highest and lowest), compute Lie (super)algebra homology and cohomology; calculate the Shapovalov determinant, and so on. It is possible to output the result in TEX format.


References in zbMATH (referenced in 25 articles , 1 standard article )

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  1. Campoamor-Stursberg, R.; Oviaño García, F.: Algorithmic construction of solvable rigid Lie algebras determined by generating functions (2022)
  2. Benayadi, Saïd; Bouarroudj, Sofiane; Hajli, Mounir: Double extensions of restricted Lie (super)algebras (2020)
  3. Bouarroudj, Sofiane; Grozman, Pavel; Lebedev, Alexei; Leites, Dimitry; Shchepochkina, Irina: Simple vectorial Lie algebras in characteristic 2 and their superizations (2020)
  4. Bouarroudj, Sofiane; Leites, Dimitry; Lozhechnyk, Olexander; Shang, Jin: The roots of exceptional modular Lie superalgebras with Cartan matrix (2020)
  5. Campoamor-Stursberg, Rutwig; Oviaño García, Francisco: Some features of rank one real solvable cohomologically rigid Lie algebras with a nilradical contracting onto the model filiform Lie algebra (Q_n) (2019)
  6. Leites, D. A.: Two problems in the theory of differential equations (2019)
  7. Benayadi, Saïd; Bouarroudj, Sofiane: Double extensions of Lie superalgebras in characteristic 2 with nondegenerate invariant supersymmetric bilinear form (2018)
  8. Bouarroudj, Sofiane; Leites, Dimitry: Invariant differential operators in positive characteristic (2018)
  9. Krutov, Andrey; Lebedev, Alexei: On gradings modulo 2 of simple Lie algebras in characteristic 2 (2018)
  10. Bouarroudj, S.; Grozman, P. Ya.; Leites, D. A.; Shchepochkina, I. M.: Minkowski superspaces and superstrings as almost real-complex supermanifolds (2012)
  11. Bouarroudj, S.; Lebedev, A. V.; Wagemann, F.: Deformations of the Lie algebra (\mathfrako(5)) in characteristics (3) and (2) (2011)
  12. Bouarroudj, Sofiane; Grozman, Pavel; Lebedev, Alexei; Leites, Dimitry: Divided power (co)homology. Presentations of simple finite dimensional modular Lie superalgebras with Cartan matrix (2010)
  13. Bouarroudj, Sofian; Grozman, Pavel; Leites, Dimitry: Defining relations of almost affine (hyperbolic) Lie superalgebras (2010)
  14. Bouarroudj, Sofiane; Grozman, Pavel; Leites, Dimitry: Classification of finite dimensional modular Lie superalgebras with indecomposable Cartan matrix (2009)
  15. Bouarroudj, S.; Grozman, P. Ya.; Leites, D. A.: New simple modular Lie superalgebras as generalized prolongs (2008)
  16. Grozman, P. Ya.; Leites, D. A.: Nonholonomic Riemann and Weyl tensors for flag manifolds (2007)
  17. Leites, Dimitry: Towards classification of simple finite dimensional modular Lie superalgebras (2007)
  18. Leites, D.: On computer-aided solving differential equations and stability study of markets (2006)
  19. Sachse, C.: Sylvester-’t Hooft generators and relations between them for (\mathfraksl(n)) and (\mathfrakgl(n| n)) (2006)
  20. Shchepochkina, I. M.: How to realize a Lie algebra by vector fields (2006)

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