ExteriorExtensions : Table of Contents

• ExteriorExtensions -- Builds a \(\mathbb{Z}_m\) -graded algebra that equivariantly extends a Lie algebra
  • exteriorExtension -- Make an extension of an exterior algebra
  • ExteriorExtension -- A new algebra constructed from the direct sum of a Lie algebra and a module
    • LieAlgebra -- a placeholder for the base Lie algebra
    • appendage -- a placeholder for the object (exterior algebra) added on to the Lie algebra by exteriorExtension
    • findGrade -- Find which graded piece of the algebra an element is in
    • HodgeStar -- The Hodge star in an exterior algebra
    • bases -- gives a list of the bases of the different graded pieces of the ExteriorExtension
    • bracket -- Compute products in an ExteriorExtension
    • ad -- Constructs the standard matrix representation of the adjoint operator
    • powerRanks -- Compute the ranks of powers of a matrix
    • powerTraces -- Compute the traces of powers of a matrix
    • getBlock -- Extract a block of the matrix representation of an adjoint operator for ExteriorExtensions
    • blockPowerRanks -- Computes a list of ranks of blocks for each power of a matrix representation of an adjoint operator for ExteriorExtensions
    • prettyBlockPowerRanks -- same as blockPowerRanks, but prettier
    • structureTensor -- Constructs the structureTensor of the ExteriorExtension
    • KillingMatrix -- Constructs the Killing matrix of the ExteriorExtension
    • LieAlg2Matrix -- Converts from the LieAlgebra to Matrix form (with the standard basis)
    • matrix2LieAlg -- Converts from Matrix form to the LieAlgebra (with the standard basis)
• getDiagonal -- Extract the diagonal of a matrix
• makeTraceless -- Project matrix to the traceless matrices.