Titlebook: Quantum Riemannian Geometry; Edwin J. Beggs,Shahn Majid Book 2020 Springer Nature Switzerland AG 2020 noncommutative geometry.quantum grou

GLOSS

pplementary material: .Combustion systems are confined fields of compressible fluids where exothermic processes of combustion take place, subject to boundary conditions imposed at its borders. The subject of .Dynamics of Combustion Systems. is presented in three parts:..Part 1. .Exothermicity. – con

CORE

Quantum Principal Bundles and Framings,udes bundles and bimodule q-monopole connections on the q- sphere, which combines with our quantum framing theory to provide our first encounter with a ’quantum Levi-Civita connection’ as a torsion free metric compatible bimodule connection on the cotangent bundle.

hedonic

Quantum Spacetime, model in the wave operator approach. We end with a brief introduction to ‘classical quantum gravity’ in the form of Poisson-Riemannian geometry and a brief introduction to the construction of quasiassociative examples by a one-sided module-algebra cochain twist.

HUMP

Book 2020 reinvention of differential geometry that refers only to the coordinate algebra, now possibly noncommutative, rather than to actual points..Such a theory is needed for the geometry of Hopf algebras or quantum groups, which provide key examples, as well as in physics to model quantum gravity effects

刺激

Differentials on an Algebra,cohomology, quantum metrics, Laplacians, and many of the key examples that will feature throughout the book. These include matrix algebras and enveloping algebras of Lie algebras as noncommutative spaces, group algebras, the algebra of functions on groups and more generally on graphs, the noncommuta

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Hopf Algebras and Their Bicovariant Calculi,co)quasitriangular case and crossed modules in the case of invertible antipode. We then cover the construction of differential structures on them and on associated algebras, including the theory of the quantum Lie algebra of a bicovariant calculus and of braided-Lie algebras in the coquasitriangular

MURAL

Vector Bundles and Connections,ive modules. The q-sphere, fuzzy sphere and q-fuzzy-sphere provide natural examples with nontrivial line bundles. The chapter also connects up via the associated projector with Connes’ approach to noncommutative geometry based on cyclic cohomology and the Chern-Connes pairing between K-theory and cy

faction

Curvature, Cohomology and Sheaves,reby provide a geometric approach to the Chern-Connes pairing more in line with Chern’s approach to characteristic classes in the classical case. We then study the cohomology of Hopf algebras and of differential sheaves, formulated as modules equipped with flat connections. We give analogues of clas

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