Israel Journal of Mathematics

, Volume 220, Issue 2, pp 791–801

Polynomial identities for matrices over the Grassmann algebra

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Abstract

We determine minimal Cayley–Hamilton and Capelli identities for matrices over a Grassmann algebra of finite rank. For minimal standard identities, we give lower and upper bounds on the degree. These results improve on upper bounds given by L. Márki, J. Meyer, J. Szigeti and L. van Wyk in a recent paper.

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References

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    L. Márki, J. Meyer, J. Szigeti and L. van Wyk, Matrix representations of finitely generated Grassmann algebras and some consequences, Israel J. Math. 208 (2015), 373–384.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 2017

Authors and Affiliations

  1. 1.Department of Algebra and Number TheoryEötvös Loránd UniversityBudapestHungary
  2. 2.Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary

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