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MP: Theoretische und Mathematische Grundlagen der Physik

MP 9: Nichtkommutative Geometrie

MP 9.1: Fachvortrag

Friday, March 19, 1999, 15:15–15:35, MA1

Supergeometry of graded matrix algebras — •Gert Reiter¹ and Harald Grosse² — ¹Technische Universität Graz, Institut für Theoretische Physik, Petersgasse 16, A-8010 Graz, Austria — ²Universität Wien, Institut für Theoretische Physik, Boltzmanngasse 5, A-1090 Wien, Austria

We develop and investigate the graded derivation-based differential calculus on the Z₂-graded algebra M(n| m) of complex (n+m) × (n+m)-matrices with “conventional block matrix grading”. In particular we show, that M(n| m) (for n≠ m) can be interpreted as “noncommutative graded manifold” in a stricter sense: There is a natural noncommutative body map and the cohomologies of M(n| m) and its body coincide (as in the case of ordinary graded manifolds).