Titlebook: Elements of Noncommutative Geometry; José M. Gracia-Bondía,Joseph C. Várilly,Héctor Fig Textbook 2001 Springer Science+Business Media New

ORBIT

Debate

率直

Noncommutative Topology: Spacesangent lines directly; but already for cubic curves it pays to examine first the ideal of all polynomials that vanish on the curve: in this way the study of an algebraic variety (the zero set of a given finite collection of polynomials) is replaced by the study of the corresponding polynomial ideal.

性上癮

雄辯

殺人

Finite-dimensional Clifford Algebras and Spinorstheir linear-algebraic and Lie-theoretic underpinnings, namely Clifford algebra. We chose not to dispense with it in this book, despite the existence of many excellent treatments, mainly for ease of reference. In particular, the infinitesimal spin representation is needed to deal with the spin conne

Anthrp

enterprise

浪費(fèi)時間

Spectral Triplesative geometry: that the structures we call geometrical are at the same time, and perhaps more fundamentally, operator-theoretic in nature. The transition to the noncommutative world entails putting the metric-generating operator front and centre. This modern approach to geometry is played out on a

有機(jī)體

Connes’ Spin Manifold Theoremrmines a unique spin structure on .; and that, among all abstract spin geometries in the sense of Section 10.5, compatible with that structure, the one determined by the Dirac operator is singled out by a variational principle.