Projective spectrum and kernel bundle

Wei He; Rong Wei Yang

doi:10.1007/s11425-015-5043-z

Projective spectrum and kernel bundle

Wei He
, Rong Wei Yang

Mathematics and Statistics

University at Albany

Southeast University, Nanjing

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

For a tuple A = (A₁,A₂, …,A_n) of elements in a unital algebra B over ℂ, its projective spectrum P(A) or p(A) is the collection of z ∈ ℂⁿ, or respectively z ∈ ℙⁿ⁻¹, such that A(z) = z₁A₁+z₂A₂+…+z_nA_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.

Original language	English
Pages (from-to)	2363-2372
Number of pages	10
Journal	Science China Mathematics
Volume	58
Issue number	11
DOIs	https://doi.org/10.1007/s11425-015-5043-z
State	Published - Nov 1 2015

Keywords

Chern character
Clifford algebra
domain of holomorphy
kernel bundle
projective spectrum

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10.1007/s11425-015-5043-z

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abstract = "For a tuple A = (A1,A2, …,An) of elements in a unital algebra B over ℂ, its projective spectrum P(A) or p(A) is the collection of z ∈ ℂn, or respectively z ∈ ℙn−1, such that A(z) = z1A1+z2A2+…+znAn is not invertible in B. The first half of this paper proves that if B is Banach then the resolvent set Pc(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.",

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N2 - For a tuple A = (A1,A2, …,An) of elements in a unital algebra B over ℂ, its projective spectrum P(A) or p(A) is the collection of z ∈ ℂn, or respectively z ∈ ℙn−1, such that A(z) = z1A1+z2A2+…+znAn is not invertible in B. The first half of this paper proves that if B is Banach then the resolvent set Pc(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.

AB - For a tuple A = (A1,A2, …,An) of elements in a unital algebra B over ℂ, its projective spectrum P(A) or p(A) is the collection of z ∈ ℂn, or respectively z ∈ ℙn−1, such that A(z) = z1A1+z2A2+…+znAn is not invertible in B. The first half of this paper proves that if B is Banach then the resolvent set Pc(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.

KW - Chern character

KW - Clifford algebra

KW - domain of holomorphy

KW - kernel bundle

KW - projective spectrum

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SP - 2363

EP - 2372

JO - Science China Mathematics

JF - Science China Mathematics

IS - 11

ER -

Projective spectrum and kernel bundle

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