Matrices over centrally \(\mathbb Z_2\)-graded rings. (English) Zbl 1016.15013

Sehgal, Sudarshan; Szigeti, Jenő

Beitr. Algebra Geom. 43, No. 2, 399-406 (2002).

The authors introduce a new computational technique for \(n\times n\) matrices over a \(\mathbb{Z}_2\)-graded ring \(R=R_0\oplus R_1\) with \(R_0\subseteq Z(R)\), leading to a new concept of the determinant which can be used to derive an invariant Cayley-Hamilton identity. An explicit construction of the inverse matrix \(A^{-1}\) for any invertible \(n\times n\) matrix \(A\) over a Grassmann algebra \(E\) is also obtained.

Reviewer: Rodica Covaci (Cluj-Napoca)

MSC:

15B33	Matrices over special rings (quaternions, finite fields, etc.)
15A24	Matrix equations and identities
15A75	Exterior algebra, Grassmann algebras
15A09	Theory of matrix inversion and generalized inverses
15A15	Determinants, permanents, traces, other special matrix functions

Keywords:

\(\mathbb Z_2\)-graded ring; skew polynomial ring; determinant and adjoint; invariant Cayley-Hamilton identity; inverse matrix; Grassmann algebra