Matrix representations of finitely generated Grassmann algebras and some consequences
Abstract
We prove that the m-generated Grassmann algebra can be embedded into a 2m-1x2m-1 matrix algebra over a factor of a commutative polynomial algebra in m indeterminates. Cayley-Hamilton and standard identities for nxn matrices over the m-generated Grassmann algebra are derived from this embedding. Other related embedding results are also presented.
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