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 13 articles , 1 standard article )

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  1. Bouarroudj, S.; Grozman, P.Ya.; Leites, D.A.; Shchepochkina, I.M.: Minkowski superspaces and superstrings as almost real-complex supermanifolds (2012)
  2. Bouarroudj, Sofiane; Grozman, Pavel; Lebedev, Alexei; Leites, Dimitry: Divided power (co)homology. Presentations of simple finite dimensional modular Lie superalgebras with Cartan matrix (2010)
  3. Bouarroudj, Sofiane; Grozman, Pavel; Leites, Dimitry: Classification of finite dimensional modular Lie superalgebras with indecomposable Cartan matrix (2009)
  4. Bouarroudj, S.; Grozman, P.Ya.; Leites, D.A.: New simple modular Lie superalgebras as generalized prolongs (2008)
  5. Grozman, P.Ya.; Leites, D.A.: Nonholonomic Riemann and Weyl tensors for flag manifolds (2007)
  6. Leites, Dimitry: Towards classification of simple finite dimensional modular Lie superalgebras (2007)
  7. Leites, D.: On computer-aided solving differential equations and stability study of markets (2006)
  8. Sachse, C.: Sylvester-’t Hooft generators and relations between them for $\germsl(n)$ and $\germgl(n\vert n)$ (2006)
  9. Shchepochkina, I.M.: How to realize a Lie algebra by vector fields (2006)
  10. Grozman, Pavel; Leites, Dimitry: Structures of $G(2)$ type and nonintegrable distributions in characteristic $p$ (2005)
  11. Grozman, Pavel; Leites, Dimitry; Shchepochkina, Irina: Defining relations for the exceptional Lie superalgebras of vector fields (2003)
  12. Burdík, Č.; Grozman, P.; Leites, D.; Sergeev, A.: Realization of Lie algebras and superalgebras in terms of creation and annihilation operators. I (2000)
  13. Grozman, P.; Leites, D.: Mathematica-aided study of Lie algebras and their cohomology -- from supergravity to ballbearings and magnetic hydrodynamics (1997)