Projective spectrum and kernel bundle

For a tuple A = ( A 1 , A 2 , …, A n ) of elements in a unital algebra B over ℂ, its projective spectrum P ( A ) or p ( A ) is the collection of z ∈ ℂ n , or respectively z ∈ ℙ n −1 , such that A ( z ) = z 1 A 1 + z 2 A 2 +…+ z n A n is not invertible in B . The first half of this paper proves that...

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Bibliographic Details
Published in:Science China. Mathematics 2015-11, Vol.58 (11), p.2363-2372
Main Authors: He, Wei, Yang, RongWei
Format: Article
Language:English
Subjects:
Algebra
Applications of Mathematics
Bundling
China
Collection
Kernels
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Vectors (mathematics)
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Summary:For a tuple A = ( A 1 , A 2 , …, A n ) of elements in a unital algebra B over ℂ, its projective spectrum P ( A ) or p ( A ) is the collection of z ∈ ℂ n , or respectively z ∈ ℙ n −1 , such that A ( z ) = z 1 A 1 + z 2 A 2 +…+ z n A n is not invertible in B . The first half of this paper proves that if B is Banach then the resolvent set P c ( A ) consists of domains of holomorphy. The second half computes the projective spectrum for the generating vectors of a Clifford algebra. The Chern character of an associated kernel bundle is shown to be nontrivial.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-015-5043-z