## $$\rho$$-differential calculi and linear connections on matrix algebra.(English)Zbl 1063.58004

Summary: We present a new aproach of the noncommutative geometry of the matrix algebra $$M_n(\mathbb{C})$$. We define two different differential calculi, and we introduce linear connections on $$M_n(\mathbb{C})$$, using the framework of $$\rho$$-algebras.

### MSC:

 58B34 Noncommutative geometry (à la Connes) 81R60 Noncommutative geometry in quantum theory

### Keywords:

noncommutative geometry
Full Text:

### References:

 [1] DOI: 10.1063/1.530888 · Zbl 0808.17011 [2] Ciupală C., Acta Math. Univ. Comenianae 72 pp 197– [3] DOI: 10.1023/B:CJOP.0000038590.53753.ef [4] DOI: 10.1063/1.528916 · Zbl 0704.53081 [5] DOI: 10.1088/0264-9381/12/6/009 · Zbl 0824.58008 [6] DOI: 10.1088/0264-9381/12/4/007 · Zbl 0822.58006 [7] DOI: 10.1016/0003-4916(87)90135-7 · Zbl 0637.17013 [8] Kastler D., Cyclic Cohomology within the Differential Envelope (1988) · Zbl 0662.55001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.