Matrix representations of finitely generated Grassmann algebras and some consequences

2013/07/01 by László Márki, Johan Meyer, Márki, László +5
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.1307.0292

to appear

arxiv created 2014/12/24 · arxiv updated 2014/12/25

Abstract

We prove that the m-generated Grassmann algebra can be embedded into a 2^m-1x2^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.

Related

• Polynomial identities for matrices over the Grassmann algebra
• Matrix identities with forms
• On the left and right coefficients of the general Cayley-Hamilton identities for an nxn matrix
• Matrices over polynomial rings approached by commutative algebra
• On the Invariants of Matrices and the Embedding Problem