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manuscripta math. 83. 365 -385 (1994) manuscripta mathematica

Summary: 1
manuscripta math. 83. 365 - 385 (1994) manuscripta
©Springer-Verlag 1994
Generic 2 x 2 Matrices With Involution
Helmer Aslaksen and Eng-Chye Tan
Procesi has given a linear basis for the ring of m generic 2 X 2 matrices.
We do the same for the ring of m generic 2 X 2 matrices with transpose
Let k be a field of characteristic 0 and let M2 = M2( k) be the
set of 2 X 2 matrices over k. Consider an involution * on M2 of
the first kind. It follows from [14] that it is sufficient to study
the symplectic involution and the transpose involution. The case
of symplectic involution is essentially treated in Section 7 of [12],
so we will only consider the transpose involution. We will use the
following notation: Mi is the set of symmetric matrices, M:; the
skew-symmetric matrices, Mf the matrices of trace 0, Mf+ the
symmetric traceless matrices and k the scalar matrices. Hence
M2 = Mi EB M2- = k EB Mf = k EB Mf+ EB M:;.


Source: Aslaksen, Helmer - Department of Mathematics, National University of Singapore


Collections: Mathematics