Mathematics – Quantum Algebra
Scientific paper
2010-12-07
Mathematics
Quantum Algebra
40 pages. Version 2 contains new references. The authors would welcome any comments on the contents or references
Scientific paper
The idea of a line bundle in classical geometry is transferred to noncommutative geometry by the idea of a Morita context. From this we can construct Z and N graded algebras, the Z graded algebra being a Hopf-Galois extension. A non-degenerate Hermitian metric gives a star structure on this algebra, and an additional star operation on the line bundle gives a star operation on the N graded algebra. In this case, we can carry out the associated circle bundle and Thom constructions. Starting with a C* algebra as base, and with some positivity assumptions, the associated circle and Thom algebras are also C* algebras. We conclude by examining covariant derivatives and Chern classes on line bundles after the method of Kobayashi and Nomizu.
Beggs Edwin J.
Brzezinski Tomasz
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