Abstract
We prove that the m-generated Grassmann algebra can be embedded into a 2m−1×2m−1 matrix algebra over a factor of a commutative polynomial algebra in m indeterminates. Cayley-Hamilton and standard identities for n × n matrices over the m-generated Grassmann algebra are derived from this embedding. Other related embedding results are also presented.
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Márki, L., Meyer, J., Szigeti, J. et al. Matrix representations of finitely generated Grassmann algebras and some consequences. Isr. J. Math. 208, 373–384 (2015). https://doi.org/10.1007/s11856-015-1203-7
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DOI: https://doi.org/10.1007/s11856-015-1203-7