K 2  of Kac–Moody groups

Matthew Westaway

doi:10.1016/j.jalgebra.2017.03.024

K 2 of Kac–Moody groups

Matthew Westaway

Mathematics

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

Abstract

Ulf Rehmann and Jun Morita, in their 1989 paper "A Matsumoto-type theorem for Kac-Moody groups", gave a presentation of K_2(A,F) for any generalised Cartan matrix A and field F. The purpose of this paper is to use this presentation to compute K_2(A,F) more explicitly in the case when A is hyperbolic. In particular, we shall show that these K_2(A,F) can always be expressed as a product of quotients of K_2(F) and K_2(2,F). Along the way, we shall also prove a similar result in the case when A has an odd entry in each column

Original language	English
Journal	Journal of Algebra
Volume	484
DOIs	https://doi.org/10.1016/j.jalgebra.2017.03.024
Publication status	Published - Aug 2017

Keywords

Kac-Moody Groups
Matsumoto’s Theorem
K_2(A, F)
K-Theory

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10.1016/j.jalgebra.2017.03.024

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title = "K 2 of Kac–Moody groups",

abstract = "Ulf Rehmann and Jun Morita, in their 1989 paper {"}A Matsumoto-type theorem for Kac-Moody groups{"}, gave a presentation of K_2(A,F) for any generalised Cartan matrix A and field F. The purpose of this paper is to use this presentation to compute K_2(A,F) more explicitly in the case when A is hyperbolic. In particular, we shall show that these K_2(A,F) can always be expressed as a product of quotients of K_2(F) and K_2(2,F). Along the way, we shall also prove a similar result in the case when A has an odd entry in each column",

keywords = "Kac-Moody Groups, Matsumoto{\textquoteright}s Theorem, K_2(A, F), K-Theory",

author = "Matthew Westaway",

year = "2017",

month = aug,

doi = "10.1016/j.jalgebra.2017.03.024",

language = "English",

volume = "484",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Elsevier",

}

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T1 - K 2 of Kac–Moody groups

AU - Westaway, Matthew

PY - 2017/8

Y1 - 2017/8

N2 - Ulf Rehmann and Jun Morita, in their 1989 paper "A Matsumoto-type theorem for Kac-Moody groups", gave a presentation of K_2(A,F) for any generalised Cartan matrix A and field F. The purpose of this paper is to use this presentation to compute K_2(A,F) more explicitly in the case when A is hyperbolic. In particular, we shall show that these K_2(A,F) can always be expressed as a product of quotients of K_2(F) and K_2(2,F). Along the way, we shall also prove a similar result in the case when A has an odd entry in each column

AB - Ulf Rehmann and Jun Morita, in their 1989 paper "A Matsumoto-type theorem for Kac-Moody groups", gave a presentation of K_2(A,F) for any generalised Cartan matrix A and field F. The purpose of this paper is to use this presentation to compute K_2(A,F) more explicitly in the case when A is hyperbolic. In particular, we shall show that these K_2(A,F) can always be expressed as a product of quotients of K_2(F) and K_2(2,F). Along the way, we shall also prove a similar result in the case when A has an odd entry in each column

KW - Kac-Moody Groups

KW - Matsumoto’s Theorem

KW - K_2(A, F)

KW - K-Theory

UR - http://dx.doi.org/10.1016/j.jalgebra.2017.03.024

UR - https://arxiv.org/abs/1607.02032

U2 - 10.1016/j.jalgebra.2017.03.024

DO - 10.1016/j.jalgebra.2017.03.024

M3 - Article

SN - 0021-8693

VL - 484

JO - Journal of Algebra

JF - Journal of Algebra

ER -

K 2 of Kac–Moody groups

Abstract

Keywords

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