대한수학회지 (Journal of the Korean Mathematical Society)

  • 제39권3호
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  • Pages.331-349
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  • 2002
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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STABLE CLASS OF EQUIVARIANT ALGEBRAIC VECTOR BUNDLES OVER REPRESENTATIONS

  • 발행 : 2002.05.01
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초록

Let G be a reductive algebraic group and let B, F be G-modules. We denote by $VEC_{G}$ (B, F) the set of isomorphism classes in algebraic G-vector bundles over B with F as the fiber over the origin of B. Schwarz (or Karft-Schwarz) shows that $VEC_{G}$ (B, F) admits an abelian group structure when dim B∥G = 1. In this paper, we introduce a stable functor $VEC_{G}$ (B, $F^{\chi}$) and prove that it is an abelian group for any G-module B. We also show that this stable functor will have nice properties.

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참고문헌

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