Matrix representations of finitely generated Grassmann algebras and some consequences

Jen\H{o} Szigeti; Johan Meyer; L\'aszl\'o M\'arki; Leon van Wyk

arxiv: 1307.0292 · v2 · pith:5ZW33M4Gnew · submitted 2013-07-01 · 🧮 math.RA · math.RT

Matrix representations of finitely generated Grassmann algebras and some consequences

L\'aszl\'o M\'arki , Johan Meyer , Jen\H{o} Szigeti , Leon van Wyk This is my paper

classification 🧮 math.RA math.RT

keywords algebragrassmannembeddingm-generatedmatrixalgebrascayley-hamiltoncommutative

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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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Matrix representations of finitely generated Grassmann algebras and some consequences

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