Witt Groups of Algebraic Groups | Zendy

Nobuaki Yagita | Zendy

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Witt Groups of Algebraic Groups

Author(s) -

Nobuaki Yagita

Publication year - 2014

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.4171/prims/126

Subject(s) - mathematics , algebraic number , algebra over a field , pure mathematics , mathematics education , mathematical analysis

Let Gk be a split reductive group over a subfield k of C corresponding to a Lie group G. Let T be a maximal torus of G. We show the isomorphism W (Gk) ∼= W (Gk/Tk) of Balmer–Witt groups. When k is algebraically closed, we prove that W (Gk) is isomorphic to the topological K-theory KO2∗−1(G/T ) of the flag manifold G/T . Then we compute it explicitly by using the fact that W (Gk) is a Hopf algebra. 2010 Mathematics Subject Classification: Primary 19G12, 55N15; Secondary 55N20.

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