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On some properties and special identities in the second order matrix algebra over Grassmann algebras

Rashkova T.

Demonstratio Mathematica

2013

Vol. 46, nr 1

29--36

The paper considers the anticommutative multiplication property for the matrix algebra M2(G) over the infinite Grassmann algebra G. We define as well some classes of ∗-symmetric and ∗ skew-symmetric matrices in (M2(G),∗) for ∗ being the transpose or the symplectic involution. As a consequence we give some ∗-identities for M2(G) of degree < 8. Examples of the application of finite-dimensional Grassmann algebras in quantum field theory are mentioned and some properties of the algebras G4 and M2(G4) are given as well.