A new determinant theory with applications
by
Jeno Szigeti
Institute of Mathematics, University of Miskolc

A new concept of determinant was introduced in [Sz1] and it turned out that by using these determinants, adjoints and characteristic polynomials a considerable part of the classical determinant theory, including the Cayley-Hamilton theorem, can be reformulated for matrices over Lie nilpotent rings. The aim of the talk is to present the so called Lie-nilpotent determinant theory and some of its applications. The applications are concerning to PI-rings ([Sz2, Sz3]), non-commutative invariant theory ([D]) and the solution of systems of linear equations over the Grassmann algebra ([SzT]).

[D] Domokos, M. Cayley-Hamilton theorem for 2x2 matrices over the Grassmann algebra, to appear in J. Pure Applied Algebra, Miskolc Conference volume [Sz1] Szigeti, J. New determinants and the Cayley-Hamilton theorem for matrices over Lie nilpotent rings, Proc. Amer. Math. Soc. (8) 125 (1997), 2245-2254. [Sz2] Szigeti, J. On the characteristic polynomial of supermatrices, to appear in Israel J. Math. [Sz3] Szigeti, J. Idempotent ideals in Lie nilpotent rings, Methods in Ring Theory eds. V. Drensky, A. Giambruno, S. Sehgal; Lecture Notes in pure and applied Mathematics, vol. 198, 287-292, Marcel Dekker 1998 [SzT] Szigeti, J. and Tuza, Zs. Solving systems of linear equations over Lie nilpotent rings, Lin. Multilin. Algebra Vol. 42., (1997), 43-51.

Date received: October 19, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabw-03.