Matrix representations of finitely generated Grassmann algebras and some consequences

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• 作者：László Márki ; Johan Meyer ; Jen? Szigeti ; Leon van Wyk
• 刊名：Israel Journal of Mathematics
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：208
• 期：1
• 页码：373-384
• 全文大小：168 KB
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• 作者单位：László Márki (1)
  Johan Meyer (2)
  Jen? Szigeti (3)
  Leon van Wyk (4)
  
  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 1364, Budapest, Pf. 127, Hungary
  2. Department of Mathematics and Applied Mathematics, University of the Free State, PO Box 339, Bloemfontein, 9300, South Africa
  3. Institute of Mathematics, University of Miskolc, 3515, Miskolc-Egyetemváros, Hungary
  4. Department of Mathematical Sciences, Stellenbosch University, P/Bag X1 Matieland 7602, Stellenbosch, South Africa
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Group Theory and Generalizations
  Analysis
  Applications of Mathematics
  Mathematical and Computational Physics
  
• 出版者：Hebrew University Magnes Press
• ISSN：1565-8511

文摘

We prove that the m-generated Grassmann algebra can be embedded into a 2 m?×2 m? 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.