ExteriorExtensions : Index

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