On $n$-homogeneous ($n\geq 4$) $C^*$-algebras over two-dimensional oriented manifolds

M. V. Shchukin

Belarusian national technical university, ul. Hmelnizkogo 9, 220013, Belarus

Abstract: Let A be a $n$-homogeneous ($n\geqslant 4$) $C^*$-algebra. Further, suppose the space $primA$ of primitive ideals for the algebra $A$ is homeomorphic to a two-dimensional oriented manifold. In this case, the algebra $A$ can be generated by three idempotents. The algebra $A$ can not be generated by two idempotents.

Keywords: $C^*$-algebra, primitive ideals, base space, algebraic bundle, operator algebra, irreducible representation.

UDC: 517.9

MSC: 46L05, 19K99

Language: English