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of line bundles. In this special case the result of any Adams operation is naturally a vector bundle, not a linear combination of ones in
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Adams operations ψ on K theory (algebraic or topological) are characterized by the following properties.
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Justification of the expected properties comes from the line bundle case, where
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or other types of algebraic construction, defined on a pattern introduced by
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Explicit Brauer
Induction: With Applications to Algebra and Number Theory
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346:{\displaystyle \chi _{\psi ^{k}(\rho )}(g)=\chi _{\rho }(g^{k})\ .}
239:). In general a mechanism for reducing to that case comes from the
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44:. The basic idea is to implement some fundamental identities in
376:. Cambridge Studies in Advanced Mathematics. Vol. 40.
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with character χ. The representation ψ(ρ) has character
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or other representing object in more abstract theories.
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Adams operations can be defined more generally in any
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186:. The idea is to apply the same polynomials to the Λ(
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104:, there is an analogy between Adams operators and
93:The fundamental idea is that for a vector bundle
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251:The Adams operation has a simple expression in
247:Adams operations in group representation theory
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415:(May 1962). "Vector Fields on Spheres".
196:. This calculation can be defined in a
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259:be a group and ρ a representation of
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204:). The polynomials here are called
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78:ψ(l)= l if l is the class of a
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138:elementary symmetric function
36:, or any allied operation in
63:Adams operations in K-theory
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378:Cambridge University Press
190:), taking the place of σ
48:theory, at the level of
370:Snaith, V. P. (1994).
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164:.) Here Λ denotes the
418:Annals of Mathematics
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253:group representation
243:for vector bundles.
237:Leray–Hirsch theorem
170:integral polynomials
149:of the roots α of a
34:topological K-theory
30:cohomology operation
469:Symmetric functions
241:splitting principle
208:(not, however, the
162:Newton's identities
464:Algebraic topology
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233:algebraic topology
210:Newton polynomials
206:Newton polynomials
73:ring homomorphisms
46:symmetric function
38:algebraic K-theory
421:. Second Series.
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413:Adams, J.F.
225:Whitney sum
108:, in which
80:line bundle
57:λ-ring
42:Frank Adams
18:mathematics
458:Categories
447:0112.38102
400:0991.20005
380:. p.
357:References
151:polynomial
116:) is to Λ(
87:functorial
317:ρ
313:χ
292:ρ
280:ψ
275:χ
235:(cf. the
216:theory).
130:power sum
180:in the σ
160:). (Cf.
28:, is a
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85:ψ are
71:ψ are
435:JSTOR
223:is a
97:on a
20:, an
386:ISBN
136:-th
128:the
443:Zbl
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396:Zbl
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212:of
124:as
32:in
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112:ψ(
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330:k
326:g
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173:Q
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156:(
154:P
143:k
140:σ
134:k
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118:V
114:V
102:X
95:V
89:.
82:.
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26:k
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