TRACE IDENTITIES FOR MATRICES WITH THE TRANSPOSE INVOLUTION

Independently, Razmyslov and Procesi have shown that for a field F of characteristic 0 all trace PIs (and thus all PIs) for M-n(F) lie in the T-ideal generated by the characteristic polynomial. Procesi then proved that for (M-n, t), an algebra with (transpose) involution, all *-trace PIs lie in the *-T-ideal generated by a set of n+1 *-trace PIs. This result proved the existence of the n+1 *-trace PIs, but no explicit formulas. In this paper we further investigate these n+1 *-trace PIs by first constructing a closely related set of so-called pure-trace *-PIs and then giving examples and applications to illuminate our results.