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$K$ -THEORY OF MONOID ALGEBRAS AND A QUESTION OF GUBELADZE

  • Amalendu Krishna (a1) and Husney Parvez Sarwar (a1)
Abstract

We show that for any commutative Noetherian regular ring $R$ containing $\mathbb{Q}$ , the map $K_{1}(R)\rightarrow K_{1}\left(\frac{R[x_{1},\ldots ,x_{4}]}{(x_{1}x_{2}-x_{3}x_{4})}\right)$ is an isomorphism. This answers a question of Gubeladze. We also compute the higher $K$ -theory of this monoid algebra. In particular, we show that the above isomorphism does not extend to all higher $K$ -groups. We give applications to a question of Lindel on the Serre dimension of monoid algebras.

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Journal of the Institute of Mathematics of Jussieu
  • ISSN: 1474-7480
  • EISSN: 1475-3030
  • URL: /core/journals/journal-of-the-institute-of-mathematics-of-jussieu
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