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arXiv · 1307.0292

Matrix representations of finitely generated Grassmann algebras and some consequences

László Márki·Johan Meyer·Jenő Szigeti·Leon van Wyk
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Abstract

We prove that the m-generated Grassmann algebra can be embedded into a 2^{m-1}x2^{m-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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László Márki, Johan Meyer, Jenő Szigeti, Leon van Wyk. 2013-07-01. Matrix representations of finitely generated Grassmann algebras and some consequences. https://arxiv.org/abs/1307.0292

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